Using the pinch technique, we determine the one-loop vertices of weak interactions in the B-LSSM and incorporate their pinch contributions into the gauge boson self-energies. Compared to the definitions of the $\textit{S}$, $\textit{T}$, and $\textit{U}$ parameters in the Standard Model based on the $S U(2)_L \otimes U(1)_Y$ group, the corresponding parameters in the local B-L gauge symmetry (B-LSSM) are modified. We present these redefined $\textit{S}$, $\textit{T}$, and $\textit{U}$ parameters and demonstrate the convergence of the results. In the framework of the low-energy effective Lagrangian for weak interactions, the $\textit{S}$, $\textit{T}$, and $\textit{U}$ parameters can be expressed as functions of specific parameters in the B-LSSM. The updated experimental and fitting results strongly constrain the parameter space of the B-LSSM.

China

Sheng-Kai Cui

Ke-Sheng Sun

Yu-Li Yan

Jin-Lei Yang

Tai-Fu Feng

$\textit{S}$, $\textit{T}$, $\textit{U}$ parameters in the B-LSSM * Supported by the Natural Science Foundation of Guangxi Autonomous Region (2022GXNSFDA035068), the Natural Science Foundation of Hebei Province (A2022104001), and the Foundation of Baoding University (2023Z01)

We consider planar $$ \mathcal{N} $$ = 4 super Yang-Mills at finite temperature with chemical potentials that couple either to the $\textit{R}$-charges or the spins of the operators. We find expressions for the Hagedorn temperatures at both zero coupling by explicitly counting states, and at strong coupling using the string theory dual. We then apply the quantum spectral curve (QSC) to this problem, which adds additional twists to the $\textit{Q}$-functions. For a single chemical potential $\textit{μ}$ coupled to one of the $\textit{R}$-charges, we find the analytic weak-coupling Hagedorn temperature to one-loop order for any value of $\textit{μ}$, and to two-loop order for $\textit{μ}$ = 1/2. We then solve the QSC numerically, showing that at strong coupling there is good agreement with the string theory prediction to order 1/$\textit{λ}$ . This provides further evidence for a recent conjecture of Harmark for the form of the world-sheet zero-point shift. We also use the QSC to find the analytic one-loop correction to the Hagedorn temperature with non-zero chemical potentials coupled to the spins.

Sweden

United Kingdom

Simon Ekhammar

United States

Joseph Minahan

Charles Thull

Twisting the Hagedorn temperature in planar $$ \mathcal{N} $$ = 4 super Yang-Mills

We present model calculations for the in-medium suppression of the Υ(1 <italic>S</italic>, 2 <italic>S</italic>, 3 <italic>S</italic>) states in <math altimg='si1.svg'><mrow><msqrt><msub><mi>s</mi><mrow><mi>N</mi><mi>N</mi></mrow></msub></msqrt><mo linebreak='goodbreak'>=</mo><mn>5.02</mn></mrow></math> TeV Pb-Pb collisions at the Large Hadron Collider in comparison with recent CMS data for all three spin-triplet <italic>s</italic>-wave states. The model parameters initial central temperature, and formation times for the &#933;( <italic>nS</italic>) states are determined in simultaneous <italic>&#967;</italic> <sup>2</sup> minimizations with respect to the data, such that the sequential centrality- and transverse-momentum-dependent suppression of the observed states is reproduced.

Germany

J. Majonica

G. Wolschin

In-medium Υ(1 <italic>S</italic>, 2 <italic>S</italic>, 3 <italic>S</italic>) suppression in Pb-Pb collisions at <math altimg='si1.svg'><mrow><msqrt><msub><mi>s</mi><mrow><mi>N</mi><mi>N</mi></mrow></msub></msqrt><mo linebreak='goodbreak'>=</mo><mn>5.02</mn></mrow></math> TeV

We compute the contour integral for the partition function of an $$ \mathcal{N} $$ = 2 SU(2) topologically twisted theory on $$ {\mathbbm{CP}}^2 $$ , dimensionally reducing from an $$ \mathcal{N} $$ = 1 theory on $\textit{S}$ . Earlier works presented the partition function as a sum over three equivariant fluxes, one for each toric divisor of $$ {\mathbbm{CP}}^2 $$ . Our result depends only on a single physical flux, assigned to the non-trivial two-cycle of the manifold. The reduced summation over fluxes is compensated by a contour of integration, arising from a different solution of the BPS equations, which captures more poles in each topological sector. As our observable involves a position-dependent Yang-Mills coupling, we compute new equivariant invariants of $$ {\mathbbm{CP}}^2 $$ , which reduce to Donaldson invariants in the non-equivariant limit. Stability conditions of gauge bundles over $$ {\mathbbm{CP}}^2 $$ appear intrinsically via the dimensional reduction.

Italy

Lorenzo Ruggeri

Contour integral for the partition function of $$ \mathcal{N} $$ = 2 topologically twisted on $$ {\mathbbm{CP}}^2 $$ and physical fluxes

<p>The effective number of neutrino species, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>N</mi><mi>eff</mi></msub></math>, serves as a key fitting parameter extensively employed in cosmological studies. In this work, we point out a fundamental inconsistency in the conventional treatment of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>N</mi><mi>eff</mi></msub></math> in big bang nucleosynthesis (BBN), particularly regarding its applicability to new physics scenarios where <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">Δ</mi><msub><mi>N</mi><mi>eff</mi></msub></math>, the deviation of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>N</mi><mi>eff</mi></msub></math> from the standard BBN prediction, is negative. To ensure consistent interpretation, it is imperative to either restrict the allowed range of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>N</mi><mi>eff</mi></msub></math> or systematically adjust neutrino-induced reaction rates based on physically motivated assumptions. As a concrete example, we consider a simple scenario in which a negative <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">Δ</mi><msub><mi>N</mi><mi>eff</mi></msub></math> arises from entropy injection into the electromagnetic sector due to the decay of long-lived particles after neutrino decoupling. This process dilutes the neutrino density and suppresses the rate of neutrino-driven neutron-proton conversion. Under this assumption, we demonstrate that the resulting BBN constraints on <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>N</mi><mi>eff</mi></msub></math> deviate significantly from those obtained by the conventional, but unphysical, extrapolation of dark radiation scenarios into the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">Δ</mi><msub><mi>N</mi><mi>eff</mi></msub><mo>&lt;</mo><mn>0</mn></math> regime.</p>

South Korea

Sougata Ganguly

Tae Hyun Jung

Seokhoon Yun

Consistent <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>N</mi><mi>eff</mi></msub></math> fitting in big bang nucleosynthesis analysis

We analyze the Macdonald’s ($\textit{q}$, $\textit{t}$)-deformed hypergeometric functions with one and two set variables and present their constraints. We prove the uniqueness to the solutions of these constraints. We propose a concise method to prove the superintegrability relations for ($\textit{q}$, $\textit{t}$)-deformed matrix models, where the constraints of hypergeometric functions play a crucial role. A conjectured superintegrability relation in the literature for the refined Chern–Simons model can be easily proved by our method. Moreover, we construct a general ($\textit{q}$, $\textit{t}$)-deformed matrix model. We give the constraint conditions for parameters in the integral. The superintegrability relations for the ($\textit{q}$, $\textit{t}$)-deformed integrals with allowed parameters are derived from the hypergeometric constraints.

Fan Liu

Rui Wang

Jie Yang

Wei-Zhong Zhao

Superintegrability for some ($\textit{q}$, $\textit{t}$)-deformed matrix models

$\textit{N}$-naturalness is a novel solution to the electroweak hierarchy problem which posits $\textit{N}$ copies of the Standard Model with varying Higgs mass-squared parameters. Reheating proceeds through a “reheaton” particle that deposits most of its energy density into the Standard Model and small but potentially measurable fractions into the other copies. Typically the sector with the lightest negative Higgs mass-squared is identified as the Standard Model. We demonstrate that $\textit{N}$-naturalness admits a broader class of realizations in which the Standard Model is identified with a heavier sector, rather than being restricted to the lightest. This is made possible by resonant mixing between the reheaton and the Higgs, which generically causes one sector to be preferentially reheated and to acquire the largest share of the energy density, singling it out as the Standard Model. We demonstrate that this scenario is consistent with current cosmological bounds on new relativistic degrees of freedom and overclosure constraints from heavy stable relics, while future cosmic microwave background and high redshift surveys will probe significant portions of the remaining parameter space. Furthermore, we highlight the possibility of a novel stochastic gravitational wave spectrum from the many cosmological first order QCD phase transitions occurring across the other sectors.

Brian Batell

Akshay Ghalsasi

Wenjie Huang

Matthew Low

$\textit{i}$-ncidental $\textit{N}$-naturalness

We continue the investigation of symmetries and anomalies of $\textit{T}$[$\textit{M}$] theories obtained by compactifying 6d SCFTs on an internal manifold $\textit{M}$. We extend the notion of “polarizations on a manifold $\textit{M}$” to cases where $\textit{M}$ may have boundaries or defects. Through examples with $\textit{M}$ of dimension two, three, and four, we illustrate recurring themes in compactifications — for instance, the important roles played by Kaluza-Klein modes, and how the generalized symmetries (including higher-group and non-invertible ones) of $\textit{T}$[$\textit{M}$], together with their anomalies, arise from non-trivial combinations of the parent 6d symmetries and the geometric structures of the internal manifold. For each dimension, we also focus on several topics that are especially interesting in that setting. These include: for 2-manifolds, the geometry of the “full moduli space” of $\textit{T}$[$\textit{M}$ ] and its interaction with polarizations and symmetries; for 3-manifolds, the effect of torsion in homology on the spectrum of line operators in $\textit{T}$[$\textit{M}$ ], together with applications to the study of quantum invariants such as $$ {\hat{Z}}_a\left({M}_3,q\right) $$ ; and for 4-manifolds, predictions for VOA[$\textit{M}$ ] following from symmetries of $\textit{T}$[$\textit{M}$ ], as well as the construction of a new invariant of 4-manifolds that depends on two “$\textit{q}$-parameters.” Along the way, we discuss a range of topics that are of independent interest, such as how non-invertible symmetries in higher dimensions can become invertible under compactification, how to classify defects in quantum field theory via their response to a change of framing, and the interplay between $$ {\hat{Z}}_a $$ and volume conjectures.

Sergei Gukov

Po-Shen Hsin

Denmark

Du Pei

Sunghyuk Park

Generalized global symmetries of $\textit{T}$[$\textit{M}$] theories. Part II

We study integrated correlation functions of half-BPS operators in SU($\textit{N}$) $$ \mathcal{N}=4 $$ supersymmetric Yang-Mills theory (SYM) involving two superconformal primary operators in the stress-tensor multiplet and two identical maximal-trace operators of arbitrary $\textit{R}$-charge $\textit{p}$. Thanks to $$ \mathcal{N}=4 $$ SYM electro-magnetic duality these integrated correlators have recently been computed as exact functions of $\textit{N}$, $\textit{p}$, and of the Yang-Mills complexified coupling $\textit{τ}$. Using a combination of tools from SL(2$\textit{,}$ ℤ) spectral theory and resurgence analysis, we study the landscape of large-$\textit{N}$ and/or large-charge expansions for these correlators. In particular, we find novel non-perturbative effects in the limit where $\textit{N}$ → ∞ with $\textit{p/N}$ fixed. From a holographic point of view this double-scaling regime is deeply connected with a second family of correlators which we analyse. Using the results for the maximal-trace operators, we derive an exact expression for a new integrated correlator involving two coherent-state operators, defined via an exponential generating function of multi-graviton states. At large-$\textit{N}$ this correlator admits a holographic dual description in terms of a back-reacted geometry known as the AdS bubble. First, we show that the leading supergravity contribution to the integrated correlator agrees with a direct explicit integration of the correlator itself. Secondly, we derive predictions for the integrated version of the Virasoro-Shapiro amplitude evaluated on the AdS bubble background. Lastly, we demonstrate that the large-$\textit{N}$ non-perturbative contributions to this integrated correlator emerge from giant-magnon configurations in the dual AdS bubble

Spain

Francesco Aprile

Daniele Dorigoni

Rudolfs Treilis

Dynamics of heavy operators in $$ \mathcal{N}=4 $$ SYM: integrated correlators and AdS bubbles

The feasibility of studying, numerically, properties of infinite volume QCD-like theories in the large $\textit{N}$ limit using coherent state variational methods is reassessed. An entirely new implementation of this approach is described, applicable to SU($\textit{N}$) lattice gauge theories, with or without fundamental representation fermions, on cubic lattices of up to four dimensions. In addition to various test cases, initial results are presented for Hamiltonian Yang-Mills theory on an infinite two-dimensional spatial lattice.

Laurence Yaffe

Resurrecting the coherent state variational algorithm for large $\textit{N}$ gauge theories