Conformal 3-point correlators of conserved currents play important roles in numerous directions. These correlators are fixed by conformal symmetry up to a few parameters, which are known only at leading order in perturbative expansions. The major challenges come from the multi-loop Feynman integrals with three external momenta. In this work, we employ the method of subgraphs to compute the subleading order corrections to the conformal current 3-point correlators in the large $\textit{N}$ expansion. We show that the method of subgraphs generates diagrammatic expansions for the conformal 3-point correlators, and that it is closely related to the operator product expansions in momentum space. We verify the subgraph expansions of conserved current 3-point correlators using exact results in 3D. We demonstrate that multi-loop 3-point Feynman integrals can be significantly simplified by taking the subgraph expansions. Due to constraints from conformal symmetry, it suffices to keep only the first few terms in the subgraph expansions to completely fix the subleading order corrections. We apply this method to compute the 1/$\textit{N}$ corrections to current correlators 〈$\textit{JJJ}$〉 in the critical $\textit{O}$($\textit{N}$) vector model and the Gross-Neveu-Yukawa model. We also compute the 1/$\textit{N}$ corrections to the coefficients in the current-current-scalar correlators 〈$\textit{JJσ}$ 〉 and 〈$\textit{JJσ}$〉 in the critical $\textit{O}$($\textit{N}$) vector model. We compare the perturbative results with the bootstrap data and discuss their application to conductivity near the quantum critical point.

China

Zhijin Li

Conformal 3-point correlators in momentum space, method of subgraphs and the 1/$\textit{N}$ expansion

Duality symmetries have been extensively investigated in various contexts, playing a crucial role in understanding quantum field theory and condensed matter theory. In this paper, we extend this framework by studying $\textit{N}$ -ality symmetries, which are a generalization of duality symmetries and are mathematically described by ℤ -graded fusion categories. In particular, we focus on an $\textit{N}$ -ality symmetry obtained by gauging a non-anomalous subgroup of ℤ × ℤ × ℤ symmetry with a type III anomaly. We determine the corresponding fusion rules via two complementary approaches: a direct calculation and a representation-theoretic method. As an application, we study the symmetry-protected topological (SPT) phases associated with the $\textit{N}$ -ality symmetry. We classify all such SPT phases using the SymTFT framework and explicitly construct lattice Hamiltonians for some of them.

Japan

Jun Maeda

Tsubasa Oishi

$\textit{N}$-ality symmetry and SPT phases in (1+1)d

We present high-precision lattice results for the confined-deconfined interface tension and the latent heat of pure <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>SU</mi><mo stretchy="false">(</mo><mi>N</mi><mo stretchy="false">)</mo></mrow></math> gauge theories up to <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>N</mi><mo>=</mo><mn>10</mn></math> and investigate their asymptotic <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>N</mi></math> dependency. For both quantities we observe the leading <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>N</mi><mn>2</mn></msup></math> behavior and subleading corrections, with the result for the interface tension <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>σ</mi><mo>/</mo><msubsup><mi>T</mi><mi>c</mi><mn>3</mn></msubsup><mo>=</mo><mn>0.0182</mn><mo stretchy="false">(</mo><mn>7</mn><mo stretchy="false">)</mo><msup><mi>N</mi><mn>2</mn></msup><mo>−</mo><mn>0.194</mn><mo stretchy="false">(</mo><mn>15</mn><mo stretchy="false">)</mo></math> and for the latent heat <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>L</mi><mo>/</mo><msubsup><mi>T</mi><mi>c</mi><mn>4</mn></msubsup><mo>=</mo><mn>0.360</mn><mo stretchy="false">(</mo><mn>6</mn><mo stretchy="false">)</mo><msup><mi>N</mi><mn>2</mn></msup><mo>−</mo><mn>1.88</mn><mo stretchy="false">(</mo><mn>17</mn><mo stretchy="false">)</mo></math>. We use the mixed phase ensemble method—where the system is constrained so that half of the volume is in the confined phase and the other half in the deconfined phase—and the interface tension is obtained by measuring the capillary wave fluctuation spectra of the interfaces between the two phases. The method bypasses supercritical slowing down from which other methods for determining the interface tension suffer, and as a by-product produces accurate estimates of the critical inverse gauge coupling as a function of the inverse temperature. We use the latter to determine the lattice beta function values, required to compute the latent heat from the discontinuity in the average plaquette action across the confined-deconfined transition.

Finland

Switzerland

Tobias Rindlisbacher

Kari Rummukainen

Ahmed Salami

Confined-deconfined interface tension and latent heat in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>SU</mi><mo stretchy="false">(</mo><mi>N</mi><mo stretchy="false">)</mo></mrow></math> gauge theory

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.

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