We consider the supersymmetric Wess-Zumino model at large $\textit{N}$ in (2 + 1) dimension. We introduce a chemical potential($\textit{μ}$) at finite temperature($\textit{T}$). The non-trivial fixed point of this model is described by a pair of coupled gap equations. This fixed point behaves as a thermal CFT for all values of the coupling. We find that at large chemical potential these coupled equations simplify and solutions become analytically tractable. We solve them analytically for all values of the coupling at this limit. The solutions admit a systematic series expansion in $$ \frac{T}{\mu } $$ . Thus, using the solutions of the gap equation at large chemical potential we can evaluate the analytic form of the partition function, stress tensor and spin-1 current as a perturbative expansion in orders of $$ \frac{T}{\mu } $$ . Applying the OPE inversion formula on the scalar and fermion two point functions of the theory, we compute higher spin currents at large $\textit{μ}$.

India

Srijan Kumar

Large $\textit{N}$ Wess-Zumino model at finite temperature and large chemical potential in 3$\textit{d}$

We analyze the supersymmetric defect indices of $$ \mathcal{N} $$ = 4 super Yang Mills theories which are simultaneously decorated by the BPS line operators and the boundary conditions. We demonstrate that the two-point functions of the boundary ’t Hooft lines of magnetic charges associated with the minuscule representations in the presence of the regular Nahm pole boundary conditions can be obtained by applying the Higgsing prescription to the half-indices of the Dirichlet boundary conditions. Accordingly, we find precise matching of the indices for pairs of the S-dual configurations with the Wilson lines and Neumann boundary conditions and those with the ’t Hooft lines and the regular Nahm pole boundary conditions. Alternatively, we analytically compute the indices by means of the inner product of the Macdonald polynomials to find the exact closed-form expressions.

Japan

Yasuyuki Hatsuda

China

Tadashi Okazaki

S-duality of boundary lines in $$ \mathcal{N} $$ = 4 SYM theories and supersymmetric indices

We study the scaling of meson-meson scattering amplitudes with the number of colors, $\textit{N}$ . We use lattice calculations in a theory with $\textit{N}$ = 4 degenerate flavors, with $\textit{N}$ = 3 – 6 and pion mass $\textit{M}$ ≈ 560 MeV. We focus on three different scattering channels, two of which have the same quantum numbers as some tetraquark candidates recently found at LHCb: the $$ {T}_{cs0}^0(2900) $$ , $$ {T}_{c\overline{s}0}^{++}(2900) $$ , $$ {T}_{c\overline{s}0}^0(2900) $$ and $$ {T}_{cs1}^0(2900) $$ states. Finite-volume energies are extracted using a large set of operators, containing two-particle operators with the form of two pions or two vector mesons, and local tetraquark operators. The resulting energy spectra is used to constrain the infinite-volume scattering amplitude by means of Lüscher’s quantization condition. We consider polynomial parametrizations of the phase shift, as well as one-loop chiral perturbation theory (ChPT) predictions. We find that our lattice results follow the expected $\textit{N}$ scaling and are sensitive to subleading $\textit{N}$ corrections. In addition, we constrain the scaling of different combinations of low-energy constants from matching to large $\textit{N}$ ChPT. The results for the channel corresponding to a $$ \left({\pi}^{+}{D}_s^{+}-{K}^{+}{D}^{+}\right) $$ state show evidence of a virtual bound state with energy $\textit{E}$ = 1.63(10)$\textit{M}$ for $\textit{N}$ = 3, while this pole disappears at $\textit{N}$ > 3. This may be connected to the exotic states found in experiment.

Germany

Spain

Jorge Baeza-Ballesteros

Pilar Hernández

United States

Switzerland

Fernando Romero-López

The $\textit{ππ}$ scattering amplitude at large $\textit{N}$

We solve models of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>N</mi></mrow></math> species of fermions in the lowest Landau level with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi mathvariant="normal">U</mi><mo stretchy="false">(</mo><mi>N</mi><mo stretchy="false">)</mo></mrow></math>-invariant interactions in the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>N</mi><mo>≫</mo><mn>1</mn></mrow></math> limit. We find saddles of the second quantized path integral at fixed chemical potential corresponding to fractional Hall states with filling <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mo stretchy="false">(</mo><mi>p</mi><mo>/</mo><mi>q</mi><mo stretchy="false">)</mo></mrow></math>, where the integers <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>p</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>q</mi></math> depend on the chemical potential and interactions. On a long torus there are <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>q</mi></math> such states related by translation symmetry, and <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>-invariant excitations of fractional charge. Remarkably, these saddles and their filling persist as extrema of the second-quantized action at <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>N</mi><mo>=</mo><mn>1</mn></math>. Our construction gives a first-principles derivation of fractional Hall states from strongly interacting fermions.

Canada

Kristan Jensen

Amir Raz

Fractional Hall Physics from Large <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>N</mi></mrow></math> Interacting Fermions

We determine the low-energy constants <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>f</mi><mn>0</mn></msub></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msubsup><mrow><mi>L</mi></mrow><mrow><mn>4</mn></mrow><mrow><mi>r</mi></mrow></msubsup></mrow></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>L</mi><mn>5</mn><mi>r</mi></msubsup></math> of SU(3) chiral perturbation theory from a lattice QCD calculation of the scalar form factors of the pion with fully controlled systematics. Lattice results are computed on a large set of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>N</mi></mrow><mrow><mi>f</mi></mrow></msub><mo>=</mo><mn>2</mn><mo>+</mo><mn>1</mn></mrow></math> gauge ensembles covering four lattice spacings <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>a</mi><mo>∈</mo><mo stretchy="false">[</mo><mn>0.049</mn><mo>,</mo><mn>0.086</mn><mo stretchy="false">]</mo><mtext> </mtext><mtext> </mtext><mi>fm</mi></mrow></math>, pion masses <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>M</mi></mrow><mrow><mi>π</mi></mrow></msub><mo>∈</mo><mo stretchy="false">[</mo><mn>130</mn><mo>,</mo><mn>350</mn><mo stretchy="false">]</mo><mtext> </mtext><mtext> </mtext><mi>MeV</mi></mrow></math>, and various large physical volumes. By determining the notorious quark-disconnected contributions with unprecedented precision and using a large range of source-sink separations <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>t</mi></mrow><mrow><mi>sep</mi></mrow></msub><mo>∈</mo><mo stretchy="false">[</mo><mn>1.0</mn><mo>,</mo><mn>3.25</mn><mo stretchy="false">]</mo><mtext> </mtext><mtext> </mtext><mi>fm</mi></mrow></math>, we are able for the first time to obtain the scalar radii from a <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>z</mi></math>-expansion parametrization of the form factors rather than a simple linear approximation at small momentum transfer. The low-energy constants are obtained from the physical extrapolation of the radii using next-to-leading-order SU(3) next-to-leading-order chiral perturbation theory to parametrize the quark mass dependence. Systematic uncertainties are estimated via model averages based on the Akaike information criterion. Our determination of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msubsup><mrow><mi>L</mi></mrow><mrow><mn>4</mn></mrow><mrow><mi>r</mi></mrow></msubsup></mrow></math> is the first lattice determination to obtain a result not compatible with zero.

Georg von Hippel

Konstantin Ottnad

Low-Energy Constants of Chiral Perturbation Theory from Pion Scalar Form Factors in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>N</mi></mrow><mrow><mi>f</mi></mrow></msub><mo>=</mo><mn>2</mn><mo>+</mo><mn>1</mn></mrow></math>-Flavor Lattice QCD with Controlled Errors

We extend the notion of chord number in the strict large $\textit{N}$ double-scaled Sachdev-Ye-Kitaev (DSSYK) model to the corresponding finite $\textit{N}$ ETH matrix model. The chord number in the strict large $\textit{N}$ DSSYK model is known to correspond to the discrete length of the Einstein-Rosen bridge in the gravity dual, which reduces to the renormalized geodesic length in JT gravity at weak coupling. At finite $\textit{N}$, these chord number states form an over-complete basis of the non-perturbative Hilbert space, as the structure of the inner product gets significantly modified due to the Cayley-Hamilton theorem: There are infinitely many null states. In this paper, by considering “EFT for gravitational observables” or a version of “non-isometric code”, we construct a family of chord number operators at finite $\textit{N}$. While the constructed chord number operator depends on the reference chord number state, it realizes approximate $\textit{q}$-deformed oscillator algebra and reproduces semiclassical bulk geometry around the reference state. As a special case, we will show that when the reference is chosen to be the chord number zero state, the chord number operator precisely matches with the Krylov state complexity, leading to the “ramp-slope-plateau” behavior at late times, implying the formation of “gray hole”.

Masamichi Miyaji

Soichiro Mori

Kazumi Okuyama

Finite $\textit{N}$ bulk Hilbert space in ETH matrix model for double-scaled SYK. Null states, state-dependence and Krylov state complexity

Field theories exhibit dramatic changes in the structure of their operator algebras in the limit where the number of local degrees of freedom (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>N</mi></math>) becomes infinite. An important example of this is that the algebras associated to local subregions may not be additively generated in the limit. We investigate examples and explore the consequences of this “superadditivity” phenomenon in large <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>N</mi></math> field theories and holographic systems. In holographic examples we find cases in which superadditive algebras can probe the black hole interior, while the additive algebra cannot. We also discuss how superaddivity explains the success of quantum error correction models of holography. Finally we demonstrate how superadditivity is intimately related to the ability of holographic field theories to perform quantum tasks that would naively be impossible. We argue that the connected wedge theorems (CWTs) of May, Penington, Sorce, and Yoshida, which characterize holographic protocols for quantum tasks, can be rephrased in terms of superadditive algebras and use this rephrasing to conjecture a generalization of the CWTs that is an equivalence statement.

Sam Leutheusser

Hong Liu

Superadditivity in large <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>N</mi></math> field theories and performance of quantum tasks

In this work, we investigate the power-expansion/OPE in super-renormalizable QFTs. In comparison to “marginal” short distance asymptotics, the power-expansion in super-renormalizable theory has a higher level of correlation with the coupling constant expansion, and the fixed-point perturbation theory for the coefficient functions suffers increasing level of IR divergences when the order of power-expansion/coupling constant expansion increases. This increasing IR sensitivity anticipates the presence of vacuum condensates of non-trivial local operators in the OPE, which not only cancel the IR divergences for coefficient functions through their UV divergences, but also shape the structure of logarithms at each power in the power-expansion. This UV-IR correspondence has been used to argue for the renormalon cancellation between coefficient functions and operators in marginal asymptotics, where the residue IR sensitivity of coefficient functions to be canceled by the operators manifests through high-order factorial growths after renormalization subtraction.

Poland

Yizhuang Liu

Renormalon-like factorial enhancements to power expansion/OPE in a super-renormalizable 2D $\textit{O}$($\textit{N}$) quartic model

We have investigated the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi mathvariant="normal">Λ</mi><mi>c</mi><mo>+</mo></msubsup><mo stretchy="false">→</mo><mi>n</mi><msup><mi>π</mi><mo>+</mo></msup><msup><mi>π</mi><mn>0</mn></msup></math> decay process using the chiral unitary approach, by considering that the nucleon resonance <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>N</mi><mo stretchy="false">(</mo><mn>1535</mn><mo stretchy="false">)</mo></math> could be dynamically generated through <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>S</mi></math>-wave pseudoscalar meson-octet baryon interactions. In the invariant mass distributions of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>π</mi><mn>0</mn></msup><mi>n</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>π</mi><mo>+</mo></msup><mi>n</mi></math>, we observe a distinct peak structure associated with the resonance states <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>N</mi><mo stretchy="false">(</mo><mn>1535</mn><msup><mo stretchy="false">)</mo><mn>0</mn></msup></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>N</mi><mo stretchy="false">(</mo><mn>1535</mn><msup><mo stretchy="false">)</mo><mo>+</mo></msup></math>, respectively. Our results suggest that the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi mathvariant="normal">Λ</mi><mi>c</mi><mo>+</mo></msubsup><mo stretchy="false">→</mo><mi>n</mi><msup><mi>π</mi><mo>+</mo></msup><msup><mi>π</mi><mn>0</mn></msup></math> process can be utilized to probe the properties of the nucleon <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>N</mi><mo stretchy="false">(</mo><mn>1535</mn><mo stretchy="false">)</mo></math>. Therefore, we encourage more precise experimental measurements of this process in the future.

Ruitian Li

Xuan Luo

Hao Sun

Theoretical study of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>N</mi><mo stretchy="false">(</mo><mn>1535</mn><mo stretchy="false">)</mo></math> in the process <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi mathvariant="normal">Λ</mi><mi>c</mi><mo>+</mo></msubsup><mo stretchy="false">→</mo><mi>n</mi><msup><mi>π</mi><mo>+</mo></msup><msup><mi>π</mi><mn>0</mn></msup></math>

We study the Higgs branch moduli space of certain 6D (1, 0) superconformal field theories (SCFTs) after gauging their <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="double-struck">Z</mi><mn>2</mn></msub></math> Green-Schwarz automorphism. We explain how to read the flavor symmetry of such SCFTs directly from the 6D construction, and we confirm the expectation by computing the Coulomb branch Hilbert series of their <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="double-struck">Z</mi><mn>2</mn></msub></math>-wreathed 3d <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="script">N</mi><mo>=</mo><mn>4</mn></math> magnetic quiver. To perform the latter computation, we explicitly introduce a methodology to determine such Hilbert series for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="double-struck">Z</mi><mn>2</mn></msub></math>-wreathed orthosymplectic quivers.

Craig Lawrie

Italy

Thekla Lepper

Alessandro Mininno

Discrete gauging of 6D SCFTs and wreathed 3D <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="script">N</mi><mo>=</mo><mn>4</mn></math> quivers