We explore the non-perturbative aspects of $\textit{c}$ = 1 string with compactified Euclidean time, its 0 + 0 dimensional matrix model duals (at self-dual radius), and 0 + 1 dimensional Matrix Quantum Mechanics (free fermion) description. We calculate the instanton normalizations, disk two-point function, and annulus one-point function in worldsheet formalism using string field theory insights. We further match them with the corresponding predictions from the matrix model descriptions. We also have some results and remarks regarding the multi ZZ instanton normalizations and the general (1, $\textit{n}$) ZZ instanton normalization for $\textit{c}$ = 1 string at both self-dual and generic radius.

India

Rishabh Kaushik

$\textit{c}$ = 1, $\textit{R}$ = 1 and $\textit{N}$ ≫ 1: ZZ instantons in 2D string theory and matrix integrals

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 $\textit{μ}$.

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

This study explores baryogenesis within a modified gravitational framework where the action incorporates a non-local kernel dependent on the Ricci scalar <italic>R</italic> and its covariant derivative &#8711; <italic>R</italic>. This extension, referred to as <math altimg='si1.svg'><mi>f</mi><mo stretchy='false'>(</mo><mi>R</mi><mo>,</mo><mi mathvariant='normal'>&#8711;</mi><mi>R</mi><mo stretchy='false'>)</mo></math> gravity, generalizes traditional <math altimg='si2.svg'><mi>f</mi><mo stretchy='false'>(</mo><mi>R</mi><mo stretchy='false'>)</mo></math> theories by introducing additional derivative terms that may influence early-universe dynamics. Within this framework, we examine four distinct forms of the cosmological scale factor: (i) an intermediate scaling solution, (ii) a conventional power-law expansion, (iii) a generalized hybrid evolution combining both power-law and exponential growth terms and (iv) logamediate scale factor. We introduce a charge-parity (CP) violating interaction term that scales linearly with the spacetime derivative of the combined Ricci scalar and its covariant derivative, expressed as <math altimg='si3.svg'><msub><mrow><mo>&#8706;</mo></mrow><mrow><mi>&#956;</mi></mrow></msub><mo stretchy='false'>(</mo><mi>R</mi><mo linebreak='badbreak' linebreakstyle='after'>+</mo><mi mathvariant='normal'>&#8711;</mi><mi>R</mi><mo stretchy='false'>)</mo></math>. Through numerical computation, we determine the resulting baryon asymmetry by evaluating the dimensionless ratio <math altimg='si4.svg'><mfrac><mrow><msub><mrow><mi>&#951;</mi></mrow><mrow><mi>B</mi></mrow></msub></mrow><mrow><mi>s</mi></mrow></mfrac></math>, where <math altimg='si5.svg'><msub><mrow><mi>&#951;</mi></mrow><mrow><mi>B</mi></mrow></msub></math> represents the baryon number density and <italic>s</italic> denotes the entropy density of the universe. We quantitatively compare our theoretical predictions for the baryon-to-entropy ratio, <math altimg='si4.svg'><mfrac><mrow><msub><mrow><mi>&#951;</mi></mrow><mrow><mi>B</mi></mrow></msub></mrow><mrow><mi>s</mi></mrow></mfrac></math>, with the current observational constraint of <math altimg='si6.svg'><mn>9.42</mn><mo>&#215;</mo><msup><mrow><mn>10</mn></mrow><mrow><mo linebreak='badbreak' linebreakstyle='after'>&#8722;</mo><mn>11</mn></mrow></msup></math>. Notably, our numerical results demonstrate remarkable agreement with this empirically established value, supporting the viability of our modified gravitational framework in explaining the observed baryon asymmetry of the universe.

Saudi Arabia

Abdulmohsen Daham Alruwaili

Azerbaijan

Pakistan

Nadeem Azhar

Abdul Jawad

Investigating baryon to entropy ratio phenomenon in <italic>f</italic>( <italic>R</italic>,&#8711; <italic>R</italic>) gravity

This study explores the structure of compact stars using an extended theory of gravity known as <math altimg='si1.svg'><mi>f</mi><mo stretchy='false'>(</mo><mi mathvariant='script'>R</mi><mo>,</mo><mi mathvariant='script'>G</mi><mo>,</mo><mi mathvariant='script'>T</mi><mo stretchy='false'>)</mo></math> gravity, where <math altimg='si3.svg'><mi mathvariant='script'>R</mi></math>, is the Ricci scalar, <math altimg='si4.svg'><mi mathvariant='script'>G</mi></math>, the Gauss-Bonnet invariant, and <math altimg='si5.svg'><mi mathvariant='script'>T</mi></math> the trace of the energy-momentum tensor. Focusing on massive radio pulsars, specifically neutron stars with masses greater than 1.8 solar masses, utilize these extreme astrophysical environments to test gravity in regimes unreachable by Earth-based experiments. We adopt a linear form of the theory, <math altimg='si18.svg'><mi>f</mi><mo stretchy='false'>(</mo><mrow><mi mathvariant='script'>R</mi><mo>,</mo><mi mathvariant='script'>G</mi><mo>,</mo><mi mathvariant='script'>T</mi></mrow><mo stretchy='false'>)</mo><mo linebreak='goodbreak' linebreakstyle='after'>=</mo><mi mathvariant='script'>R</mi><mo linebreak='goodbreak' linebreakstyle='after'>+</mo><mi>&#945;</mi><mi mathvariant='script'>G</mi><mo linebreak='goodbreak' linebreakstyle='after'>+</mo><mi>&#946;</mi><mi mathvariant='script'>T</mi></math>, with <italic>&#945;</italic>, <cross-ref refid='fn0010' id='crf0390'>1</cross-ref> and <italic>&#946;</italic> are dimensional constants, and derive an exact analytical solution for anisotropic perfect fluid spheres in hydrostatic equilibrium. This model incorporates the compactness factor <math altimg='si7.svg'><mi>C</mi><mo linebreak='goodbreak' linebreakstyle='after'>=</mo><mfrac><mrow><mn>2</mn><mi>G</mi><mi>M</mi></mrow><mrow><mi>R</mi><msup><mrow><mi>c</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow></mfrac></math>, to describe all physical properties within the stellar interior. To constrain the model, we employ observational data from the pulsar <italic>U</italic>1724, using its mass and radius to fix the parameters at their upper bounds: <math altimg='si8.svg'><msub><mrow><mi>&#945;</mi></mrow><mrow><mn>1</mn></mrow></msub><mo linebreak='goodbreak' linebreakstyle='after'>=</mo><mfrac><mrow><mi>&#945;</mi></mrow><mrow><msup><mrow><mi>R</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow></mfrac><mo linebreak='goodbreak' linebreakstyle='after'>=</mo><mo>&#177;</mo><mn>0.023</mn></math> and <math altimg='si9.svg'><msub><mrow><mi>&#946;</mi></mrow><mrow><mn>1</mn></mrow></msub><mo linebreak='goodbreak' linebreakstyle='after'>=</mo><mfrac><mrow><mi>&#946;</mi></mrow><mrow><msup><mrow><mi>&#954;</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow></mfrac><mo linebreak='goodbreak' linebreakstyle='after'>=</mo><mo>&#177;</mo><mn>0.001</mn></math>. The resulting model is consistent with physical viability and observational constraints. Notably, the squared sound speed in this framework remains below the theoretical limit ( <math altimg='si10.svg'><mmultiscripts><mrow><mtext mathvariant='normal'>c</mtext></mrow><mrow><mi>s</mi></mrow><none /><none /><mrow><mn>2</mn></mrow></mmultiscripts><mo linebreak='goodbreak' linebreakstyle='after'>&lt;</mo><msup><mrow><mi>c</mi></mrow><mrow><mn>2</mn></mrow></msup><mo stretchy='false'>/</mo><mn>3</mn></math>), contrasting with general relativity results. Without assuming a specific equation of state, the model exhibits linear behavior and predicts a core density several times higher than nuclear saturation density ( <math altimg='si11.svg'><msub><mrow><mi>&#961;</mi></mrow><mrow><mtext>nuc</mtext></mrow></msub><mo linebreak='goodbreak' linebreakstyle='after'>=</mo><mn>2.6</mn><mo>&#215;</mo><msup><mrow><mn>10</mn></mrow><mrow><mn>14</mn></mrow></msup></math> g/cm 3), with surface density <math altimg='si12.svg'><msub><mrow><mi>&#961;</mi></mrow><mrow><mi>s</mi></mrow></msub></math>, also exceeding this threshold. Additionally, the derived mass-radius relation agrees well with existing astrophysical observations.

Egypt

South Africa

G.G.L. Nashed

Constraining linear form of <math altimg='si1.svg'><mi>f</mi><mo stretchy='false'>(</mo><mrow><mi mathvariant='script'>R</mi><mo>,</mo><mi mathvariant='script'>G</mi><mo>,</mo><mi mathvariant='script'>T</mi></mrow><mo stretchy='false'>)</mo></math> gravity from astrophysical observations of the Pulsar U1724

In this paper, we investigate Friedmann Robertson Walker (FRW) space time filled with a perfect fluid in <math altimg='si1.svg'><mi>f</mi><mo stretchy='false'>(</mo><mi>R</mi><mo>,</mo><msub><mrow><mi>L</mi></mrow><mrow><mi>m</mi></mrow></msub><mo stretchy='false'>)</mo></math> modified theory framework formulated by Harko and Lobo (2010), where <italic>R</italic> is the Ricci scalar curvature, <math altimg='si2.svg'><msub><mrow><mi>L</mi></mrow><mrow><mi>m</mi></mrow></msub></math> is the ideal fluid's Lagrangian. Two specific non-linear <math altimg='si1.svg'><mi>f</mi><mo stretchy='false'>(</mo><mi>R</mi><mo>,</mo><msub><mrow><mi>L</mi></mrow><mrow><mi>m</mi></mrow></msub><mo stretchy='false'>)</mo></math> functional forms are assumed: <math altimg='si3.svg'><mi>f</mi><mo stretchy='false'>(</mo><mi>R</mi><mo>,</mo><msub><mrow><mi>L</mi></mrow><mrow><mi>m</mi></mrow></msub><mo stretchy='false'>)</mo><mo linebreak='goodbreak' linebreakstyle='after'>=</mo><mfrac><mrow><mi>R</mi></mrow><mrow><mn>2</mn></mrow></mfrac><mo linebreak='goodbreak' linebreakstyle='after'>+</mo><mo stretchy='false'>(</mo><mn>1</mn><mo linebreak='badbreak' linebreakstyle='after'>+</mo><mi>&#945;</mi><mi>R</mi><mo stretchy='false'>)</mo><msub><mrow><mi>L</mi></mrow><mrow><mi>m</mi></mrow></msub></math> representing a non-minimal coupling case and <math altimg='si4.svg'><mi>f</mi><mo stretchy='false'>(</mo><mi>R</mi><mo>,</mo><msub><mrow><mi>L</mi></mrow><mrow><mi>m</mi></mrow></msub><mo stretchy='false'>)</mo><mo linebreak='goodbreak' linebreakstyle='after'>=</mo><mfrac><mrow><mi>R</mi></mrow><mrow><mn>2</mn></mrow></mfrac><mo linebreak='goodbreak' linebreakstyle='after'>+</mo><msubsup><mrow><mi>L</mi></mrow><mrow><mi>m</mi></mrow><mrow><mi>n</mi></mrow></msubsup><mo linebreak='goodbreak' linebreakstyle='after'>+</mo><mi>&#946;</mi></math> representing a minimal coupling case. Here, we use a cubic parametrization of the deceleration parameter that produces an accelerating universe to obtain the exact solution for the field equations. We investigate the evolution of cosmological parameters including pressure and energy density. Using <math altimg='si5.svg'><msub><mrow><mi>L</mi></mrow><mrow><mi>m</mi></mrow></msub><mo linebreak='goodbreak' linebreakstyle='after'>=</mo><mi>&#961;</mi></math> and a cubic parametrization of the deceleration parameter to account for late-time cosmic acceleration. We analyze the evolution of cosmological parameters in terms of both cosmic time and redshift and constrain model parameters using observational datasets from <math altimg='si6.svg'><mi>H</mi><mo stretchy='false'>(</mo><mi>z</mi><mo stretchy='false'>)</mo></math>, Pantheon, BAO, H(z)+Pantheon, H(z)+BAO+Pantheon. The results show a transition of the deceleration parameter from deceleration to acceleration and indicate a possible quintessence-like behavior at the present epoch. The findings suggest that the proposed models can effectively describe the universe's expansion history in agreement with observations.

Kangujam Priyokumar Singh

Syed Sabanam

Anil Kumar Yadav

Asem Jotin Meitei

Modeling through the cubic parametrization of the deceleration parameter in <italic>f</italic>( <italic>R</italic>, <italic>Lm</italic>) gravity with observational constraints