Within the framework of Dyson-Schwinger equations (DSEs) and by means of the Multiple Reflection Expansion approximation, we study the finite volume effects on the constituent quark mass in a strong external magnetic field. Since the magnetic field influences the coupling constant, which controls the strength of strong interactions in QCD, we adopt the magnetic-field-dependent running coupling constant in our simulations. The results show that, in addition to the magnetic field, the masses of constituent quarks also have a significant dependence on the volume and the running coupling constant. The model behaves closely to the infinite volume limit for large sizes, but the effect of the finite volume is significant when the system size $\textit{R}$ is about $ 2-6 $ fm. The finite volume effects and the magnetic-field-dependent running coupling constant have considerable influence on the phase transition.

China

Li-Juan Zhou

De-Xian Wei

Zhong-Yi Liu

Hong-Wei Zhong

Dynamical quark mass and finite volume effects in the Dyson-Schwinger equations * Li-Juan Zhou has been supported by the National Natural Science Foundation of China (11865005), the Natural Science Foundation of Guangxi (China) (2025GXNSFAA069552). De-Xian Wei has been supported by the National Natural Science Foundation of China (12105057), the Natural Science Foundation of Guangxi (China) (2023GXNSFAA026020)

We compute the phase of the Euclidean gravity partition function on manifolds of the form $\textit{S}$ × $\textit{M}$ . We find that the total phase is equal to the phase in pure gravity on $\textit{S}$ times an extra phase that arises from negative mass squared fields that we obtain when we perform a Kaluza-Klein reduction to $\textit{S}$ . The latter can be matched to the phase expected for physical negative modes seen by a static path observer in $\textit{dS}$ . In the case of $\textit{S}$ × $\textit{S}$ the answer can be interpreted in terms of a computation in the static patch of $\textit{dS}$ or $\textit{dS}$ . We also provide the phase when we have a product of many spheres. We clarify the procedure for determining the precise phase factor. We discuss some aspects of the interpretation of this phase.

United States

Victor Ivo

Juan Maldacena

Zimo Sun

Physical instabilities and the phase of the Euclidean path integral

I derive a new charge constraint in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mfrac><mrow><mn>1</mn></mrow><mrow><mn>16</mn></mrow></mfrac></mrow></math>-Bogomol’nyi-Prasad-Sommerfield sectors of the Berenstein, Maldacena, and Nastase supersymmetric, gauged <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>U</mi><mo stretchy="false">(</mo><mi>N</mi><mo stretchy="false">)</mo></math> matrix quantum mechanics. It was previously shown that the supersymmetric index of the model exhibits an exponential dependence on <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>N</mi><mn>2</mn></msup></math> from the vacuum that preserves the full gauge group. I show that the reality of the associated entropy implies that the Cartan of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>S</mi><mi>O</mi><mo stretchy="false">(</mo><mn>3</mn><mo stretchy="false">)</mo></math> vanishes for any <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mfrac><mn>1</mn><mn>16</mn></mfrac></math>-Bogomol’nyi-Prasad-Sommerfield sector with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>U</mi><mo stretchy="false">(</mo><mi>N</mi><mo stretchy="false">)</mo></math> gauge symmetry. The Berenstein-Maldacena-Nastase charge constraint could be useful to determine whether there exists a dual supersymmetric black hole solution asymptoting to a plane-wave background.

Yoav Zigdon

Charge constraint in the Berenstein-Maldacena-Nastase model

We define the “squared amplitudes” in planar Aharony-Bergman-Jafferis-Maldacena theory, analogous to those in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi mathvariant="script">N</mi><mo>=</mo><mn>4</mn></mrow></math> super-Yang-Mills (SYM) theory. Surprisingly, the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>n</mi></mrow></math>-point <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>L</mi></math>-loop integrands with fixed <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>N</mi><mo>≔</mo><mi>n</mi><mo>+</mo><mi>L</mi></mrow></math> are unified in a single generating function. Similar to the SYM four-point half–Bogomol’nyi-Prasad-Sommerfield correlator integrand, the generating function enjoys a hidden <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>S</mi><mi>N</mi></msub></math> permutation symmetry in the dual space, allowing us to write it as a linear combination of weight-3 planar <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>f</mi></math> graphs. Remarkably, through Gram identities it can also be represented as a linear combination of “bipartite” <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>f</mi></math> graphs that manifest the important property that no odd-multiplicity amplitude exists in the theory. The generating function and these properties are explicitly checked against squared amplitudes for all <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>n</mi></math> with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>N</mi><mo>=</mo><mn>4</mn></math>, 6, 8. By drawing analogies with SYM, we conjecture some “graphical rules” the generating function satisfies, and exploit them to bootstrap a unique <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>N</mi><mo>=</mo><mn>10</mn></math> result, which provides new results for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>n</mi><mo>=</mo><mn>10</mn></math> squared tree amplitudes, as well as integrands for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mo stretchy="false">(</mo><mi>n</mi><mo>,</mo><mi>L</mi><mo stretchy="false">)</mo><mo>=</mo><mo stretchy="false">(</mo><mn>4</mn><mo>,</mo><mn>6</mn><mo stretchy="false">)</mo><mo>,</mo><mo stretchy="false">(</mo><mn>6</mn><mo>,</mo><mn>4</mn><mo stretchy="false">)</mo></mrow></math>. Our results strongly suggest the existence of a “bipartite correlator” in Aharony-Bergman-Jafferis-Maldacena theory that unifies all squared amplitudes and satisfies physical constraints underlying these graphical rules.

Song He

Canxin Shi

Yichao Tang

Yao-Qi Zhang

Hidden Permutation Symmetry of Squared Amplitudes in Aharony-Bergman-Jafferis-Maldacena Theory

In this work, we bootstrap the 4-point correlators on the 1D celestial circle using 3D symmetries in the Aharony-Bergman-Jafferis-Maldacena theory as constraints. We find that the dual inversion property is strong enough to replace the crossing symmetry condition (or cyclic invariant condition) when bootstrapping. We also give some results about the conformal block expansion coefficients which contain the spectrum. Furthermore, we extract the OPE spectrum from the multi-collinear limit since all 3-point ABJM amplitudes vanish. Although we studied a specific theory, the methods used are valid for more general cases.

Yi-Xiao Tao

The Aharony-Bergman-Jafferis-Maldacena theory on a circle

We investigate the thermal phase structure of the Berenstein-Maldacena-Nastase matrix model using nonperturbative lattice Monte Carlo calculations. Our main analyses span 3 orders of magnitude in the coupling, involving systems with sizes up to <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>N</mi><mi>τ</mi></msub><mo>=</mo><mn>24</mn></math> lattice sites 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> gauge groups with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>8</mn><mo>≤</mo><mi>N</mi><mo>≤</mo><mn>16</mn></math>. In addition, we carry out extended checks of discretization artifacts for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>N</mi><mi>τ</mi></msub><mo>≤</mo><mn>128</mn></math> and gauge group SU(4). We find results for the deconfinement temperature that interpolate between the perturbative prediction at weak coupling and the large-<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>N</mi></math> dual supergravity calculation at strong coupling. While we confirm that the phase transition is first order for strong coupling, it appears to be continuous for weaker couplings.

Raghav G. Jha

South Africa

Anosh Joseph

United Kingdom

David Schaich

Finite-temperature phase diagram of the Berenstein-Maldacena-Nastase matrix model on the lattice

We investigate the large-<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>N</mi></mrow></math> limit of the Berenstein-Maldacena-Nastase (BMN) matrix model with classical bosonic membranes which have spherical topologies and spin inside the 11-dimensional maximally supersymmetric plane-wave background. First we classify all possible M2-brane configurations based on the distribution of their components inside the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>S</mi><mi>O</mi><mo stretchy="false">(</mo><mn>3</mn><mo stretchy="false">)</mo><mo>×</mo><mi>S</mi><mi>O</mi><mo stretchy="false">(</mo><mn>6</mn><mo stretchy="false">)</mo></math> symmetric plane-wave spacetime. We then formulate a number of simple but very representative Ansätze of dielectric tops that rotate in this space. We examine the leading-order radial and angular/multipole stability for a wide range of these configurations. By analyzing perturbations at the next-to-leading order, we find that they exhibit the phenomenon of turbulent cascading of instabilities. Thereby, long-wavelength perturbations generate higher-order multipole instabilities through their nonlinear couplings.

Greece

Minos Axenides

Emmanuel Floratos

South Korea

Georgios Linardopoulos

Turbulent aspects of Berenstein-Maldacena-Nastase membrane dynamics

We discuss a no-boundary proposal for a subregion of the universe. In the classical approximation, this density matrix involves finding a specific classical solution of the equations of motion with no boundary. Beyond the usual no boundary condition at early times, we also have another no boundary condition in the region we trace out. We can find the prescription by starting from the usual Hartle-Hawking proposal for the wavefunction on a full slice and tracing out the unobserved region in the classical approximation. We discuss some specific subregions and compute the corresponding solutions. These geometries lead to phenomenologically unacceptable probabilities, as expected.

Yue-Zhou Li

The no boundary density matrix

We investigate the correlators of three single-trace operators in Aharony-Bergman-Jafferis-Maldacena (ABJM) theory from the perspective of integrable boundary states. Specifically, we focus on scenarios where two operators are 1/3-BPS and the entire correlation function is considered within the twisted-translated frame. The correlator can be expressed as the overlap between a boundary state and a Bethe state. It is found that the boundary state formed by the two 1/3-BPS operators is integrable when the number of Wick contractions between the non-BPS operator and one of the 1/3-BPS operators is 0 or 1. We compute the overlaps for the proven integrable cases utilizing the symmetries and the coordinate Bethe ansatz.

Jun-Bao Wu

Peihe Yang

Three-point functions in Aharony-Bergman-Jafferis-Maldacena theory and integrable boundary states

We show that the Banks-Fischler-Shenker-Susskind matrix model for M-theory obeys the leading and subleading soft theorems expected from eleven-dimensional supergravity. The subleading soft theorem implies the amplitude is Lorentz symmetric. This is argued for general four point amplitudes, but only for restricted kinematics for five and higher point amplitudes.