We show that the Seiberg-type duality of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi mathvariant="script">N</mi><mo>=</mo><mn>1</mn></mrow></math> gauge theory coupled with tensor chiral fields and fundamental chiral fields works if the meson spectrum built from the tensor fields takes a particular form: (a) It should be truncated. (b) The <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>R</mi></math> charges of tensor fields <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo stretchy="false">{</mo><msub><mi>R</mi><mi>a</mi></msub><mo stretchy="false">}</mo></math> and the truncated mesons <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo stretchy="false">{</mo><msub><mi>R</mi><mi>j</mi></msub><mo stretchy="false">}</mo></math> take very special values. The meson spectrum so that the duality works is encoded elegantly in the factorization of the polynomial <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>y</mi><mi>n</mi></msup><mo>−</mo><mn>1</mn><mo>=</mo><msub><mi mathvariant="normal">Φ</mi><mo>+</mo></msub><msub><mi mathvariant="normal">Φ</mi><mo>−</mo></msub></math>. Our consideration covers many known <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="script">N</mi><mo>=</mo><mn>1</mn></math> dualities and generates a large class of new examples.

China

Yuanyuan Fang

Jing Feng

Dan Xie

Duality of four dimensional <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="script">N</mi><mo>=</mo><mn>1</mn></math> gauge theory

In this paper we analyze the 2 + 1d conformal fixed points arising from SU($\textit{N}$ ) Chern-Simons-matter theories with multiple flavors $\textit{N}$ $\textit{ >}$ 1 in the ’t Hooft large $\textit{N}$ limit. The multi-flavor generalization of quasi-fermionic theories (fermions or critical scalars coupled to Chern-Simons gauge fields) is straightforward, but this is not true for quasi-bosonic theories (scalars or critical fermions coupled to Chern-Simons gauge fields). The latter theories have three flavor-singlet relevant operators and also three marginal operators, that become exactly marginal for infinite $\textit{N}$ , but have a non-zero beta function at order 1$\textit{/N}$ . We compute the beta functions of these couplings in various weak coupling limits, and also discuss their general structure, generalizing previous computations for $\textit{N}$ = 1. We find that IR-stable fixed points of the marginal couplings exist for some values of $\textit{N}$ and of the ’t Hooft coupling $\textit{λ}$, but not for other values, and in one case we can explicitly follow how two pairs of fixed points merge and disappear as $\textit{λ}$ is increased. We also analyze the “Semi-Critical” conformal field theories that arise when fine-tuning two (rather than three) relevant operators, and compute the beta function for their (single) marginal coupling constant.

Israel

Ofer Aharony

Ronny Frumkin

Jonathan Mehl

Large $\textit{N}$ Chern-Simons-matter fixed points with multiple flavors

We determine the scaling dimensions in the boundary CFT corresponding to the O($\textit{N}$) model in EAdS . The CFT data accessible to the 4-point boundary correlator of fundamental fields are extracted in $\textit{d}$ = 2 and $\textit{d}$ = 4, at a finite coupling, and to the leading nontrivial order in the 1$\textit{/N}$ expansion. We focus on the non-singlet sectors, namely the anti-symmetric and symmetric traceless irreducible representations of the O($\textit{N}$) group, extending the previous results that considered only the singlet sector. Studying the non-singlet sector requires an understanding of the crossed-channel diagram contributions to the $\textit{s}$-channel conformal block decomposition. Building upon an existing computation, we present general formulas in $\textit{d}$ = 2 and $\textit{d}$ = 4 for the contribution of a $\textit{t}$-channel conformal block to the anomalous dimensions of $\textit{s}$-channel double-twist operators, derived for external scalar operators with equal scaling dimensions. Up to some technical details, this eventually leads to the complete picture of 1$\textit{/N}$ corrections to the CFT data in the interacting theory.

Czechia

Jonáš Dujava

Petr Vaško

Finite-coupling spectrum of O($\textit{N}$) model in AdS

We investigate the fully supersymmetric solutions in a class of $$\mathcal{N}=3$$ and $$\mathcal{N}=4$$ higher derivative Poincaré supergravity theories. These class of theories are obtained within the framework of conformal supergravity using the standard Weyl multiplet and contains a set of terms related to the Weyl square term by supersymmetry. We work in the superconformal formalism and show that flat spacetime is the only fully supersymmetric solution in these theories. However, in $$\mathcal{N}=2$$ Poincaré supergravity theories that falls into the same class, two fully supersymmetric stationary solutions exist: Bertotti-Robinson geometry ($\textit{AdS}$ × $\textit{S}$ ) and flat spacetime, which are known in the literature. We discuss the reason behind the richer vacua in $$\mathcal{N}=2$$ supergravity compared to its $$\mathcal{N}=3$$ and $$\mathcal{N}=4$$ cousins.

India

Abhinava Bhattacharjee

Germany

Subramanya Hegde

Bindusar Sahoo

Only flat spacetime is full BPS in four dimensional $$\mathcal{N}=3$$ and $$\mathcal{N}=4$$ supergravity

We study large-<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>N</mi><mi>c</mi></msub></math> scalar <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>QCD</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow></math>, a <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>1</mn><mo>+</mo><mn>1</mn></math>-dimensional confining gauge theory with fundamental scalar quarks, whose meson spectrum is governed by a Bethe-Salpeter equation structurally parallel to the ’t Hooft equation. Exploiting this structural analogy, we develop a nonperturbative analytic framework, based on integrability and inspired by the Fateev-Lukyanov-Zamolodchikov (FLZ) method, originally devised for the ’t Hooft model and later extended in our previous works. Notably, the same Bethe-Salpeter equation also arises in the description of interchain mesons in the doubled Ising model coupled via a spin-spin interaction term. Within the FLZ approach, we find spectral sums and derive a systematic large-<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>n</mi></math> WKB expansion for the meson spectrum. The analytic results reproduce the expected behavior in key asymptotic regimes, such as the near-critical limit <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>m</mi><mo stretchy="false">→</mo><mi>g</mi><mo>/</mo><msqrt><mi>π</mi></msqrt></math> and the heavy-quark regime <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>m</mi><mo>≫</mo><mi>g</mi></mrow></math>, and are in good agreement with numerical data. Finally, by analytically continuing the mass parameter into the complex plane, we uncover two infinite families of singularities where individual mesons become massless, suggesting a hidden connection to nontrivial conformal field theories.

United States

Pavel Meshcheriakov

Analytical results for large-<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>N</mi><mi>c</mi></msub></math> scalar <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>QCD</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow></math>

Models with classically degenerate vacua often support quasiclassical configurations of nontrivial topology. In (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>0</mn><mo>+</mo><mn>1</mn></mrow></math>)-dimensional quantum mechanics with a double-well potential, for example, instantons induce mixing between the two perturbative ground states in the purely bosonic case, while in the supersymmetric version, the tunneling amplitude is suppressed. In this work, we investigate (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>1</mn><mo>+</mo><mn>1</mn></mrow></math>)-dimensional models featuring classically Bogomol’nyi-Prasad-Sommerfield saturated kinks with degenerate masses and identical topology. Recent studies suggest that such kinks may undergo mixing mediated by scalar-field instantons. We analyze this phenomenon in a supersymmetric framework and demonstrate that, whereas mixing indeed occurs in the bosonic theory, the presence of fermionic zero modes in the supersymmetric case leads to the vanishing of the transition amplitude. To illustrate these results, we examine two examples featuring Wess-Zumino models with two and four supercharges. The latter example is motivated by the Affleck-Dine-Seiberg superpotential. We also present a number of developments of instanton calculus in the case of instantons in kink backgrounds.

Evgenii Ievlev

Mikhail Shifman

Degenerate kinks and kink-instantons in two-dimensional scalar field models with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mrow><mi mathvariant="script">N</mi></mrow><mo>=</mo><mn>1</mn></mrow></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi mathvariant="script">N</mi><mo>=</mo><mn>2</mn></mrow></math> supersymmetry

In this study, we conduct a thorough examination of the spectrum of the open confining string in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>3</mn><mo>+</mo><mn>1</mn></mrow></math> dimensions, commonly referred to as the open flux tube, across various gauge groups of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>S</mi><mi>U</mi><mo stretchy="false">(</mo><msub><mi>N</mi><mi>c</mi></msub><mo stretchy="false">)</mo></math>. Our primary objective is to explore its behavior as we approach the large-<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>N</mi><mi>c</mi></msub></math> limit and the identification of possible world-sheet axion states. Specifically, we undertake a detailed analysis of the associated spectrum for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>N</mi><mi>c</mi></msub><mo>=</mo><mn>3</mn></math>, 4, 5, 6. This marks the first systematic investigation of the open flux-tube spectrum within the context of the large-<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>N</mi><mi>c</mi></msub></math> limit. More specifically, we analyze the spectra of flux tubes that form between a static quark-antiquark pair, considering a significant number of radial excitations and eight irreducible representations characterized by the quantum numbers of angular momentum <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">Λ</mi></math>, charge conjugation and parity <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>η</mi><mrow><mi>C</mi><mi>P</mi></mrow></msub></math>, and the reflection symmetry <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ε</mi></math> for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">Λ</mi><mo>=</mo><mn>0</mn></math>. To this purpose we employ a diverse set of suitable operators, an anisotropic action, and smearing techniques, and solve the generalized eigenvalue problem. We compare our findings with predictions from the Nambu-Goto string model to assess potential tensions indicative of novel phenomena such as the existence of axionlike state along the flux-tube world sheet. Notably, we provide undoubted evidence of the existence of a massive axionlike particle with the same mass as the corresponding axion extracted within the context of closed flux tube. This strengthens the conjecture that the axion is a property of the world sheet of the QCD string.

Portugal

Alireza Sharifian

Cyprus

Andreas Athenodorou

Pedro Bicudo

Spectrum of open confining strings in the large-<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>N</mi><mi>c</mi></msub></math> limit

We revisit the contribution of the QCD <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mover accent="true"><mi>θ</mi><mo stretchy="false">¯</mo></mover></math> term to the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math>-violating pion-nucleon couplings and the nucleon electric dipole moment in a combined large-<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>N</mi><mi>c</mi></msub></math> and chiral perturbation theory framework. In particular, we approach this issue through the emergent spin-flavor symmetry of the baryon sector at large but finite <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>N</mi><mi>c</mi></msub></math>. We obtain good agreement with previous analyses for the pion-nucleon couplings and show that the large-<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>N</mi><mi>c</mi></msub></math> framework indicates that tree-level contributions to the electric dipole moment possibly play a dominant role. The spin-flavor symmetry also enables us to provide novel constraints on <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math>-violating pion-<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">Δ</mi></math> couplings, as well as the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">Δ</mi></math> electric dipole moment and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">Δ</mi><mi>N</mi></math> transition moment.

Thomas R. Richardson

Strong <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math> violation and large-<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>N</mi><mi>c</mi></msub></math> spin-flavor symmetry

We numerically study <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi mathvariant="double-struck">Z</mi></mrow><mrow><mi>N</mi></mrow></msub></mrow></math> lattice gauge theories in 4D as prototypical models of systems with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="double-struck">Z</mi><mi>N</mi></msub></math> 1-form symmetry. For <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>N</mi><mo>≥</mo><mn>3</mn></mrow></math>, we provide evidence that such systems exhibit not only the expected phases with spontaneously broken/restored symmetry but also a third photon phase. When present, the 1-form symmetry provides a precise notion of confinement, and it is commonly believed that confinement ensues due to the proliferation of extended, stringlike objects known as center vortices, which carry a <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="double-struck">Z</mi><mi>N</mi></msub></math> flux. However, this picture is challenged by the three-phase scenario investigated here. We show that both the confined and the photon phases are associated with the proliferation of center vortices and that the key difference between them lies in whether or not vortex junctions—the monopoles— proliferate.

United Kingdom

Jeffrey Giansiracusa

David Lanners

Tin Sulejmanpasic

Emergent Photons and Confinement: A Numerical Study on <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi mathvariant="double-struck">Z</mi></mrow><mrow><mi>N</mi></mrow></msub></mrow></math> Lattice Gauge Theory

We consider correlation functions in symmetric product orbifold CFTs on the sphere, focusing on the case where all operators are single-cycle twists, and the covering surface is also a sphere. We directly construct the general class of covering space maps where there are three twists of arbitrary lengths, along with any number of twist-2 insertions. These are written as a ratio of sums of Jacobi polynomials with ∆$\textit{N}$ + 1 coefficients $\textit{b}$ , which parametrize the ∆$\textit{N}$ cross ratios. These coefficients have a scaling symmetry $\textit{b}$ → $\textit{λb}$ , making them naturally valued in $$ {\mathbbm{CP}}^{\Delta N} $$ . We explore limits where various ramified points on the cover approach each other, which are understood as crossing channel specific OPE limits, and find that these limits are defined by algebraic varieties of $$ {\mathbbm{CP}}^{\Delta N} $$ . We compute the expressions needed to calculate the group element representative correlation functions for bare twists. Specializing to the cases ∆$\textit{N}$ = 1, 2, we find closed form for these expressions which define four- and five-point functions of bare twists.

Benjamin Burrington

Ida Zadeh

Covering space maps for $\textit{n}$-point functions with three long twists