Based on a sample of $2.7\times10^{9}$ $\psi(3686)$ events collected by the BESIII detector operating at the BEPCII collider, the decay $\psi(3686)\to\gamma\chi_{cJ}, \chi_{cJ}\to\eta\eta\eta^{\prime}$ is analyzed. The decay modes $\chi_{c1}$ and $\chi_{c2}\to\eta\eta\eta^{\prime}$ are observed for the first time, and their corresponding branching fractions are determined to be ${\cal{B}}(\chi_{c1}\to\eta\eta\eta^{\prime}) = $ $ (1.40\, \pm 0.13\, (\text{stat.}) \pm 0.09\, (\text{sys.})) \times 10^{-4}$ and ${\cal{B}}(\chi_{c2}\to\eta\eta\eta^{\prime}) = (4.18\, \pm 0.84\, (\text{stat.}) \pm 0.48\, (\text{sys.})) \times 10^{-5}$ . An upper limit on the branching fraction of $\chi_{c0}\to\eta\eta\eta^{\prime}$ is set as $2.59 \times 10^{-5}$ at a 90% confidence level (CL). A partial wave analysis (PWA) of the decay $\chi_{c1}\to\eta\eta\eta^{\prime}$ is performed to search for the $1^{-+}$ exotic state $\eta_1(1855)$ . The PWA result indicates that the structure in the $\eta\eta^{\prime}$ mass spectrum is attributed to $f_0(1500)$ , while in the $\eta\eta$ mass spectrum, it is attributed to the $0^{++}$ phase space. The upper limit of ${\cal{B}}(\chi_{c1}\to\eta_{1}(1855)\eta) \cdot {\cal{B}}(\eta_{1}(1855)\to\eta\eta^{\prime}) \lt $ $ 9.79 \times 10^{-5}$ is set based on the PWA at 90% CL.

China

M. Ablikim

Russia

M.N. Achasov

Sweden

P. Adlarson

X.C. Ai

Germany

R. Aliberti

Italy

A. Amoroso

Q. An

Y. Bai

O. Bakina

Y. Ban

H.R. Bao

Poland

V. Batozskaya

Mongolia

K. Begzsuren

N. Berger

M. Berlowski

M. Bertani

D. Bettoni

F. Bianchi

E. Bianco

A. Bortone

I. Boyko

United States

R.A. Briere

A. Brueggemann

H. Cai

M.H. Cai

X. Cai

A. Calcaterra

G.F. Cao

N. Cao

Türkiye

S.A. Cetin

X.Y. Chai

J.F. Chang

G.R. Che

Y.Z. Che

C.H. Chen

Chao Chen

G. Chen

H.S. Chen

H.Y. Chen

M.L. Chen

S.J. Chen

S.L. Chen

S.M. Chen

T. Chen

X.R. Chen

X.T. Chen

X.Y. Chen

Y.B. Chen

Y.Q. Chen

Z. Chen

Z.J. Chen

Z.K. Chen

S.K. Choi

X. Chu

G. Cibinetto

F. Cossio

United Kingdom

J. Cottee-Meldrum

J.J. Cui

H.L. Dai

J.P. Dai

A. Dbeyssi

R.E. de Boer

D. Dedovich

C.Q. Deng

Z.Y. Deng

A. Denig

I. Denysenko

M. Destefanis

F. De Mori

B. Ding

X.X. Ding

Y. Ding

Y.X. Ding

J. Dong

L.Y. Dong

M.Y. Dong

X. Dong

M.C. Du

S.X. Du

Y.Y. Duan

P. Egorov

G.F. Fan

J.J. Fan

Y.H. Fan

J. Fang

S.S. Fang

W.X. Fang

Y.Q. Fang

R. Farinelli

L. Fava

F. Feldbauer

G. Felici

C.Q. Feng

J.H. Feng

L. Feng

Q.X. Feng

Search for $\textit{η}$ $_{1}$(1855) in $\textit{χ}$ $\textit{cJ}$ → $\textit{ηηη}$′ decays * Supported in part by National Key R&D Program of China (2023YFA1606000, 2023YFA1606704); National Natural Science Foundation of China (NSFC) (11635010, 11935015, 11935016, 11935018, 12025502, 12035009, 12035013, 12061131003, 12192260, 12192261, 12192262, 12192263, 12192264, 12192265, 12221005, 12225509, 12235017, 12361141819); the Chinese Academy of Sciences (CAS) Large-Scale Scientific Facility Program; CAS (YSBR-101); 100 Talents Program of CAS; The Institute of Nuclear and Particle Physics (INPAC) and Shanghai Key Laboratory for Particle Physics and Cosmology; Agencia Nacional de Investigación y Desarrollo de Chile (ANID), Chile (ANID PIA/APOYO AFB230003); German Research Foundation DFG (FOR5327); Istituto Nazionale di Fisica Nucleare, Italy; Knut and Alice Wallenberg Foundation (2021.0174, 2021.0299); Ministry of Development of Turkey (DPT2006K-120470); National Research Foundation of Korea ( NRF-2022R1A2C1092335); National Science and Technology fund of Mongolia; National Science Research and Innovation Fund (NSRF) via the Program Management Unit for Human Resources Institutional Development, Research and Innovation of Thailand ( B50G670107); Polish National Science Centre (2024/53/B/ST2/00975); Swedish Research Council (2019.04595); U. S. Department of Energy (DE-FG02-05ER41374)

The Tambara-Yamagami (TY) fusion category symmetry $$ \textrm{TY}\left(\mathbbm{A},\chi, \epsilon \right) $$ describes the enhanced non-invertible self-duality symmetry of a 2-dim QFT under gauging a finite Abelian group $$ \mathbbm{A} $$ . We generalize the enhanced non-invertible symmetries by considering twisted gauging which allows stacking $$ \mathbbm{A} $$ -SPTs before and after the gauging. Such noninvertible symmetries can be obtained from invertible anyon permutation symmetries of the 3-dim SymTFT. Consider a finite group $\textit{G}$ formed by (un)twisted gaugings of $$ \mathbbm{A} $$ , a 2-dim QFT invariant under topological manipulations in $\textit{G}$ admits non-invertible $\textit{G-ality defects}$. We study the classification and the physical implication of the $\textit{G}$-ality defects using the SymTFT and the group-theoretical fusion categories, with three concrete examples. 1) Triality with $$ \mathbbm{A} $$ = $\textit{ℤ}$ × $\textit{ℤ}$ where $\textit{N}$ is coprime with 3. The classification was previously determined by Jordan and Larson where the data is similar to the TY fusion categories, and we determine the anomaly of these fusion categories. 2) $\textit{p}$-ality with $$ \mathbbm{A} $$ = $\textit{ℤ}$ × $\textit{ℤ}$ where $\textit{p}$ is an odd prime. We consider two such categories $$ {\mathcal{P}}_{\pm, m} $$ which are distinguished by different choices of the symmetry fractionalization, a new data that does not appear in the TY classification, and show that they have distinct anomaly structures and spin selection rules. 3) $\textit{S}$ -ality with $$ \mathbbm{A} $$ = $\textit{ℤ}$ × $\textit{ℤ}$ . We study their classification explicitly for $\textit{N}$ < 20 via SymTFT, and provide a group-theoretical construction for certain $\textit{N}$. We find $\textit{N}$ = 5 is the minimal $\textit{N}$ to admit an $\textit{S}$ -ality and $\textit{N}$ = 11 is the minimal $\textit{N}$ to admit a group-theoretical $\textit{S}$ -ality.

Da-Chuan Lu

Zhengdi Sun

Zipei Zhang

Exploring $\textit{G}$-ality defects in 2-dim QFTs

Using <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="script">N</mi><mo>=</mo><mn>1</mn></math> supersymmetric QCD (SQCD) as a prototype model, this work presents a formulation of overlap quarks and gluinos on the lattice, with particular emphasis on the construction of chirally symmetric Yukawa terms. By incorporating the Ginsparg-Wilson relation, chiral transformations, and the Majorana condition for gluinos, we construct a consistent framework that preserves a lattice-modified chiral symmetry and reduces the number of required counterterms compared to Wilson-type discretizations. The formulation introduces auxiliary fermionic fields to realize exact chiral symmetry in Yukawa interactions and enables a detailed analysis of the resulting matrix structures. Upon functionally integrating out the auxiliary fields, ultralocal interaction terms emerge as new contributions to the lattice action. This approach provides a robust foundation for nonperturbative lattice studies of supersymmetric gauge theories. Future work will focus on computing all perturbative fine-tunings required in this formulation to enable continuum matching and numerical simulations of SQCD.

Cyprus

M. Costa

E. Ioannou

H. Panagopoulos

<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi mathvariant="script">N</mi><mo>=</mo><mn>1</mn></mrow></math> supersymmetric QCD on the lattice using overlap fermions

The infinite series of 4D <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="script">N</mi><mo>=</mo><mn>2</mn></math> superconformal field theories with central charge relation <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>a</mi><mrow><mn>4</mn><mi mathvariant="normal">D</mi></mrow></msub><mo>=</mo><msub><mi>c</mi><mrow><mn>4</mn><mi mathvariant="normal">D</mi></mrow></msub></math> are closely related to the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="script">N</mi><mo>=</mo><mn>4</mn></math> super Yang-Mills theory. In this paper, we study the modular properties of their associated vertex operator algebras <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="double-struck">V</mi><mo stretchy="false">[</mo><msub><mi mathvariant="script">T</mi><mrow><mi>p</mi><mo>,</mo><mi>N</mi></mrow></msub><mo stretchy="false">]</mo></math>, where <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="script">T</mi><mrow><mi>p</mi><mo>,</mo><mi>N</mi></mrow></msub></math> are those <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>a</mi><mo>=</mo><mi>c</mi></math> theories with an <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>S</mi><mi>U</mi><mo stretchy="false">(</mo><mi>N</mi><mo stretchy="false">)</mo></math> gauge group. We exploit the closed-form formula for the Schur index of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="script">N</mi><mo>=</mo><mn>4</mn></math> <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>S</mi><mi>U</mi><mo stretchy="false">(</mo><mi>N</mi><mo stretchy="false">)</mo></math> theories <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="script">T</mi><mrow><mi>S</mi><mi>U</mi><mo stretchy="false">(</mo><mi>N</mi><mo stretchy="false">)</mo></mrow></msub></math> to derive the space of characters of the vertex operator algebra <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="double-struck">V</mi><mo stretchy="false">[</mo><msub><mi mathvariant="script">T</mi><mrow><mi>p</mi><mo>,</mo><mi>N</mi></mrow></msub><mo stretchy="false">]</mo></math> and the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>S</mi></mrow></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>T</mi></mrow></math> matrices, and find the (nonmonic) modular linear differential equations that constrain the module characters when possible. We investigate the geometric interpretation of some of these modular data from the viewpoint of 4D mirror symmetry. Using insights from the flavored modular differential equation and defect index, we investigate a map between module characters of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="double-struck">V</mi><mo stretchy="false">[</mo><msub><mi mathvariant="script">T</mi><mrow><mi>S</mi><mi>U</mi><mo stretchy="false">(</mo><mi>N</mi><mo stretchy="false">)</mo></mrow></msub><mo stretchy="false">]</mo></math> and those of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="double-struck">V</mi><mo stretchy="false">[</mo><msub><mi mathvariant="script">T</mi><mrow><mi>p</mi><mo>,</mo><mi>N</mi></mrow></msub><mo stretchy="false">]</mo></math>.

Yiwen Pan

Peihe Yang

Modularity, 4d mirror symmetry, and vertex operator algebra modules of 4D <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi mathvariant="script">N</mi><mo>=</mo><mn>2</mn></mrow></math> SCFTs with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>a</mi><mo>=</mo><mi>c</mi></math>

In our previous work [<a href="http://dx.doi.org/10.1103/PhysRevC.101.014003">Phys. Rev. C 101, 014003 (2020)</a>], we analyzed all available data on differential cross sections and spin density matrix elements for the <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>γ</mi><mi>p</mi><mo>→</mo><msup><mi>K</mi><mrow><mo>*</mo><mo>+</mo></mrow></msup><mi mathvariant="normal">Λ</mi></mrow></math> reaction using an effective Lagrangian approach. There, the <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math>-channel <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>K</mi><mo>,</mo><mo> </mo><msup><mi>K</mi><mo>*</mo></msup></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>κ</mi></math> exchanges, the <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>u</mi></math>-channel <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">Λ</mi><mo>,</mo><mo> </mo><mi mathvariant="normal">Σ</mi></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi mathvariant="normal">Σ</mi><mo>*</mo></msup></math> exchanges, the <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi></math>-channel <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>N</mi><mo>,</mo><mo> </mo><mrow><mi>N</mi><mrow><mo>(</mo><mn>2060</mn><mo>)</mo></mrow><mn>5</mn><mo>/</mo><msup><mn>2</mn><mo>−</mo></msup></mrow></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>N</mi><mrow><mo>(</mo><mn>2000</mn><mo>)</mo></mrow><mn>5</mn><mo>/</mo><msup><mn>2</mn><mo>+</mo></msup></mrow></math> exchanges, and the interaction current were taken into account in constructing the reaction amplitudes. It was found that, overall, the agreement of the theoretical results with the corresponding data is fairly good. However, noticeable discrepancies between the model results and the data on spin density matrix elements <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>ρ</mi><mn>00</mn></msub></math> are still observed in the center-of-mass energy region around <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>W</mi><mo>≈</mo><mn>2.08</mn></mrow></math> GeV, indicating the need for additional reaction mechanisms. On the other hand, the hidden-strange pentaquark-like state <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>N</mi><mrow><mo>(</mo><mn>2080</mn><mo>)</mo></mrow><mn>3</mn><mo>/</mo><msup><mn>2</mn><mo>−</mo></msup></mrow></math>, which is proposed to be a <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msup><mi>K</mi><mo>*</mo></msup><mi mathvariant="normal">Σ</mi></mrow></math> molecular state as the strange partner of the <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msub><mi>P</mi><mi>c</mi></msub><mrow><mo>(</mo><mn>4457</mn><mo>)</mo></mrow></mrow></math> hadronic molecule, has been found to play quite active roles in reproducing the data for <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msup><mi>K</mi><mrow><mo>*</mo><mo>+</mo></mrow></msup><msup><mi mathvariant="normal">Σ</mi><mn>0</mn></msup></mrow><mo>,</mo><mo> </mo><mrow><msup><mi>K</mi><mrow><mo>*</mo><mn>0</mn></mrow></msup><msup><mi mathvariant="normal">Σ</mi><mo>+</mo></msup></mrow></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>ϕ</mi><mi>p</mi></mrow></math> photoproduction reactions. Based on these observations, in the present work, we reanalyze the data for the <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>γ</mi><mi>p</mi><mo>→</mo><msup><mi>K</mi><mrow><mo>*</mo><mo>+</mo></mrow></msup><mi mathvariant="normal">Λ</mi></mrow></math> reaction by incorporating the pentaquark-like state <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>N</mi><mrow><mo>(</mo><mn>2080</mn><mo>)</mo></mrow><mn>3</mn><mo>/</mo><msup><mn>2</mn><mo>−</mo></msup></mrow></math> in our previously proposed model. The results show that, with the inclusion of the contributions of <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>N</mi><mrow><mo>(</mo><mn>2080</mn><mo>)</mo></mrow><mn>3</mn><mo>/</mo><msup><mn>2</mn><mo>−</mo></msup></mrow></math>, the quality of the theoretical description of the <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>γ</mi><mi>p</mi><mo>→</mo><msup><mi>K</mi><mrow><mo>*</mo><mo>+</mo></mrow></msup><mi mathvariant="normal">Λ</mi></mrow></math> data can be considerably improved. In particular, the data on spin density matrix elements <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>ρ</mi><mn>00</mn></msub></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>Re</mi><mspace width="0.16em"></mspace><msub><mi>ρ</mi><mn>10</mn></msub></mrow></math> in the near-threshold energy region are significantly better reproduced. This achievement indicates that the hypothesis of the <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>N</mi><mrow><mo>(</mo><mn>2080</mn><mo>)</mo></mrow><mn>3</mn><mo>/</mo><msup><mn>2</mn><mo>−</mo></msup></mrow></math> molecular state is compatible with the available data for the <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>γ</mi><mi>p</mi><mo>→</mo><msup><mi>K</mi><mrow><mo>*</mo><mo>+</mo></mrow></msup><mi mathvariant="normal">Λ</mi></mrow></math> reaction. The reaction mechanism of <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>γ</mi><mi>p</mi><mo>→</mo><msup><mi>K</mi><mrow><mo>*</mo><mo>+</mo></mrow></msup><mi mathvariant="normal">Λ</mi></mrow></math> is analyzed and the <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>N</mi><mrow><mo>(</mo><mn>2080</mn><mo>)</mo></mrow><mn>3</mn><mo>/</mo><msup><mn>2</mn><mo>−</mo></msup></mrow><mo>,</mo><mo> </mo><mrow><mi>N</mi><mrow><mo>(</mo><mn>2060</mn><mo>)</mo></mrow><mn>5</mn><mo>/</mo><msup><mn>2</mn><mo>−</mo></msup></mrow><mo>,</mo><mo> </mo><mrow><mi>N</mi><mrow><mo>(</mo><mn>2000</mn><mo>)</mo></mrow><mn>5</mn><mo>/</mo><msup><mn>2</mn><mo>+</mo></msup></mrow></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>K</mi></math> exchanges are found to provide dominant contributions.

Wen-Ya Tian

Neng-Chang Wei

Yu-Fei Wang

Fei Huang

Bing-Song Zou

Effects of the hadronic molecule <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>N</mi><mrow><mo>(</mo><mn>2080</mn><mo>)</mo></mrow><mn>3</mn><mo>/</mo><msup><mn>2</mn><mo>−</mo></msup></mrow></math> on <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msup><mi>K</mi><mrow><mo>*</mo><mo>+</mo></mrow></msup><mi mathvariant="normal">Λ</mi></mrow></math> photoproduction

We consider a neutrinophilic <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>U</mi><mo stretchy="false">(</mo><mn>1</mn><mo stretchy="false">)</mo></math> extension of the Standard Model (SM) under which only a second Higgs doublet and SM singlet scalars and fermions are charged. The new gauge boson <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>Z</mi><mo>′</mo></msup></math> couples to the SM minimally, generated by <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Z</mi><mo>−</mo><msup><mi>Z</mi><mo>′</mo></msup></math> mixing. As the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>Z</mi><mo>′</mo></msup></math> is very weakly coupled, it can mostly be produced through the decay of the scalars from the second Higgs doublet at the Large Hadron Collider (LHC). We discuss the scalar sector of the model in detail and consider decay modes such as <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo stretchy="false">(</mo><msup><mi>H</mi><mo>±</mo></msup><mo stretchy="false">→</mo><msup><mi>W</mi><mo>±</mo></msup><msup><mi>Z</mi><mo>′</mo></msup><mo>,</mo><msub><mi>h</mi><mn>2</mn></msub><mo stretchy="false">→</mo><mi>V</mi><mi>V</mi><mo>,</mo><mo stretchy="false">(</mo><mi>V</mi><mo>=</mo><msup><mi>W</mi><mo>±</mo></msup><mo>,</mo><mi>Z</mi><mo>,</mo><msup><mi>Z</mi><mo>′</mo></msup><mo stretchy="false">)</mo><mo>,</mo><msub><mi>A</mi><mn>2</mn></msub><mo stretchy="false">→</mo><msub><mi>h</mi><mn>1</mn></msub><msup><mi>Z</mi><mo>′</mo></msup><mo stretchy="false">(</mo><mi>Z</mi><mo stretchy="false">)</mo><mo stretchy="false">)</mo></math> that lead to multilepton signals at the LHC from the pair production of the scalars. We analyze the signal with a representative value of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>Z</mi><mo>′</mo></msup></math> mass to show the discovery potential of the two-Higgs doublet model scalars at the LHC.

India

Anjan Kumar Barik

Santosh Kumar Rai

Agnivo Sarkar

LHC signals for a 2HDM with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>Z</mi><mo>′</mo></msup></math> in a neutrinophilic <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>U</mi><mo stretchy="false">(</mo><mn>1</mn><mo stretchy="false">)</mo></math> model

It has been shown that the non-Abelian vortex string in 4D <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="script">N</mi><mo>=</mo><mn>2</mn></math> supersymmetric QCD (SQCD) with the U(2) gauge group and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>N</mi><mi>f</mi></msub><mo>=</mo><mn>4</mn></math> flavors becomes a critical superstring. Its 10D target space is a product of the flat 4D space and an internal noncompact Calabi-Yau threefold, namely, the conifold. It was also shown that the Coulomb branch of the associated string sigma model, which opens up at strong coupling, can be described by <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="script">N</mi><mo>=</mo><mn>2</mn></math> Liouville theory. We continue here the study of the recently proposed mass deformation of the U(2) theory with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>N</mi><mi>f</mi></msub><mo>=</mo><mn>4</mn></math>, interpolating to SQCD with the U(4) gauge group and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>N</mi><mi>f</mi></msub><mo>=</mo><mn>8</mn></math> quarks, by analyzing the mass-deformed <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="script">N</mi><mo>=</mo><mn>2</mn></math> Liouville theory on the string world sheet, and show that it is always described by the trumpet geometry of the target space, which is <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>T</mi></math>-dual to the 2D <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="script">N</mi><mo>=</mo><mn>2</mn></math> supersymmetric black hole. We use this correspondence to find the low-lying hadron spectrum in the deformed SQCD, and explain the expected increase in the number of hadronic states in the theory with more gauge fields and quarks by considering the near-Hagedorn behavior of the 2D black hole.

Evgenii Ievlev

Andrei Marshakov

Gleb Sumbatian

Alexei Yung

Critical non-Abelian vortex string and 2D <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="script">N</mi><mo>=</mo><mn>2</mn></math> black hole

We propose a computation of curvature of arbitrary two-dimensional surfaces of three-dimensional objects, which is a contribution to discrete gravity with potential applications in network geometry. We begin by linking each point of the surface in question to its four closest neighbors, forming quads. We then focus on the simplices of $$d=2$$ , or triangles embedded in these quads, which make up a pure simplicial complex with $$d=2$$ . This allows us to numerically compute the local metric along with zweibeins, which subsequently leads to a derivation of discrete curvature defined at every triangle or face. We provide an efficient algorithm with $$\mathscr {O}(N \log {N})$$ complexity that first orients two-dimensional surfaces, solves the nonlinear system of equations of the spin-connections resulting from the torsion condition, and returns the value of curvature at each face.

Lebanon

Ali Chamseddine

Ola Malaeb

Sara Najem

Curvature of an arbitrary surface for discrete gravity and for $$d=2$$ pure simplicial complexes

We study the scalar curvature $\textit{R}$ of the vector moduli space of 5d $$\mathcal{N}=1$$ supergravities, obtained by compactifying M-theory on a Calabi-Yau three-fold. We find that $\textit{R}$ can only diverge at points where some gauge interactions go to infinite coupling in Planck units and become SCFTs or LSTs decoupled from gravity and other vector multiplets. For 5d SCFTs of rank $\textit{r}$ ≤ 2 divergences occur if, additionally, the SCFT still couples to the vevs of such vector multiplets, so that along its Coulomb branch its gauge kinetic matrix and/or string tensions depend on some non-dynamical parameters. If the strong coupling singularity is better understood as a 6d (1$\textit{,}$ 0) SCFT, as in some decompactification limits, then divergences in $\textit{R}$ arise when the SCFT is endowed with a non-Abelian gauge group.

Spain

Alejandro Blanco

Fernando Marchesano

Luca Melotti

Curvature divergences in 5d $$\mathcal{N}=1$$ supergravity

In this work, we present the exact solution of a static, spherically symmetric black hole embedded in a Dehnen $$\left( 1,4,\frac{1}{2}\right) $$ dark matter halo. We explore both its optical and thermodynamic properties. Using the principle of least action, we derive the null geodesics to analyze and illustrate the corresponding gravitational lensing and light ring phenomena in the presence of the dark matter halo. We then turn to the thermodynamics of the black hole–dark matter system, examining the mass function, entropy, temperature, heat capacity, and Gibbs free energy to assess both local and global stability. Our results show that the surrounding dark matter halo plays a crucial role: it not only enhances the thermodynamic stability of the black hole but also enables the occurrence of phase transitions.

Thailand

David Senjaya

Black hole in Dehnen $$\left( 1,4,\frac{1}{2}\right) $$ dark matter halo: exact solution, lensing, light ring, and thermodynamics