arXiv subjects
Publications and source records attributed to Anosh Joseph.
Over the last twenty years, work based on lattice supersymmetry has generated many new results and insights into the non-perturbative nature of string theory, quantum black holes, and gravity. This endeavor is a broad research program encompassing lattice field theory, supersymmetry, string theory, and quantum gravity. In this volume, we look at a selected subset of the topics covering recent progress in lattice supersymmetry and holography.
We investigate non-perturbative supersymmetry breaking in various models of quantum mechanics, including an interesting class of $PT$-invariant models, using lattice path integrals. These theories are discretized on a temporal Euclidean lattice with anti-periodic boundary conditions. Hybrid Monte Carlo algorithm is used to update the field configurations to their equilibrium values. We used the Ward identities and expectation values of superpotentials as tools for probing supersymmetry breaking.
The IKKT matrix model, in the large-$N$ limit, is conjectured to be a non-perturbative definition of the ten-dimensional type IIB superstring theory. In this work, we investigate the possibility of spontaneous breaking of the ten-dimensional rotational symmetry in the Euclidean IKKT model. Since the effective action, after integrating out the fermions, is inherently complex, we use the complex Langevin dynamics to study the model. In order to evade the singular-drift problem in the model, we add supersymmetry preserving deformations and then take the vanishing limit of the deformations. Our analysis suggests that the phase of the Pfaffian indeed induces the spontaneous SO(10) symmetry breaking in the Euclidean IKKT model.
We study the bosonic part of the BMN matrix model for wide ranges of temperatures, values of the deformation parameter, and numbers of colors $16 \leq N \leq 48$. Using lattice computations, we analyze phase transitions in the model, observing a single first-order transition from a uniform to a gapped phase for all values of the deformation parameter. We study the functional form of the dependence of the critical temperature on the deformation parameter, to describe how our results smoothly interpolate between the limits of the bosonic BFSS model and the gauged Gaussian model.
Self-interacting scalar quantum field theories possessing $PT$-symmetry are physically admissible since their energy spectrum is real and bounded below. However, models with $PT$-invariant potentials can have complex actions in general and a non-perturbative study of such systems using methods based on traditional Monte Carlo is hindered due to numerical sign problem. In this work we employ complex Langevin based on stochastic quantization to study two-dimensional scalar field theories, including the ones exhibiting $PT$-symmetry. We also study the simplest supersymmetric version of these systems and address the question on dynamical supersymmetry breaking.
We present our current results from ongoing lattice investigations of the Berenstein--Maldacena--Nastase deformation of maximally supersymmetric Yang--Mills quantum mechanics. We focus on the thermal phase structure of this theory, which depends on both the temperature $T$ and the deformation parameter $μ$, through the dimensionless ratios $T / μ$ and $g = λ/ μ^3$ with $λ$ the 't Hooft coupling. We determine the critical $T / μ$ of the confinement transition for couplings $g$ that span three orders of magnitude, to connect weak-coupling perturbative calculations and large-$N$ dual supergravity predictions in the strong-coupling limit. Analyzing multiple lattice sizes up to $N_τ = 24$ and numbers of colors up to $N = 16$ allows initial checks of the large-$N$ continuum limit.
Using complex Langevin method we probe the possibility of dynamical supersymmetry breaking in supersymmetric quantum mechanics models with complex actions. The models we consider are invariant under the combined operation of parity and time reversal, in addition to supersymmetry. When actions are complex traditional Monte Carlo methods based on importance sampling fail. Models with dynamically broken supersymmetry can exhibit sign problem due to the vanishing of the partition function. Complex Langevin method can successfully evade the sign problem. Our simulations suggest that complex Langevin method can reliably predict the absence or presence of dynamical supersymmetry breaking in these one-dimensional models with complex actions.
We study the two-dimensional Yang--Mills theory with four supercharges in the large-$N$ limit. By using thermal boundary conditions, we analyze the internal energy and the distribution of scalars. We compare their behavior to the maximally supersymmetric case with sixteen supercharges, which is known to admit a holographic interpretation. Our lattice results for the scalar distribution show no visible dependence on $N$ and the energy at strong coupling appears independent of temperature.
We introduce and discuss Monte Carlo methods in quantum field theories. Methods of independent Monte Carlo, such as random sampling and importance sampling, and methods of dependent Monte Carlo, such as Metropolis sampling and Hamiltonian Monte Carlo, are introduced. We review the underlying theoretical foundations of Markov chain Monte Carlo. We provide several examples of Monte Carlo simulations, including one-dimensional simple harmonic oscillator, unitary matrix model exhibiting Gross-Witten-Wadia transition and a supersymmetric model exhibiting dynamical supersymmetry breaking.
In this paper, by analyzing the underlying Lefschetz thimble structure, we study quantum phases in zero-dimensional scalar field theories with complex actions. Using first principles, we derive the Lefschetz thimble equations of these models, and discuss the issues when we apply the same calculations for more complicated systems. We also derive the conditional expressions involving relations among the parameters of the model, that would help us predict quantum phase transitions in these systems.
We present initial results from ongoing lattice investigations into the thermal phase structure of the Berenstein--Maldacena--Nastase deformation of maximally supersymmetric Yang--Mills quantum mechanics. The phase diagram of the theory depends on both the temperature $T$ and the deformation parameter $μ$, through the dimensionless ratios $T / μ$ and $g \equiv λ/ μ^3$ with $λ$ the 't Hooft coupling. Considering couplings $g$ that span three orders of magnitude, we reproduce the weak-coupling perturbative prediction for the deconfinement $T / μ$ and approach recent large-$N$ dual supergravity analyses in the strong-coupling limit. We are carrying out calculations with lattice sizes up to $N_τ = 24$ and numbers of colors up to $N = 16$, to allow initial checks of the large-$N$ continuum limit.
We investigate the possibility of spontaneous supersymmetry breaking in a class of zero-dimensional ${\cal N} = 2$ supersymmetric quantum field theories, with complex actions, using complex Langevin dynamics and stochastic quantization. Our simulations successfully capture the presence or absence of supersymmetry breaking in these models. The expectation value of the auxiliary field under twisted boundary conditions was used as an order parameter to capture spontaneous supersymmetry breaking in these models.
Using complex Langevin dynamics we examine the phase structure of complex unitary matrix models and compare the numerical results with analytic results found at large $N$. The actions we consider are manifestly complex, and thus the dominant contribution to the path integral comes from the space of complexified gauge field configuration. For this reason, the eigenvalues of unitary matrix lie off the unit circle and venture out in the complex plane. One example of a complex unitary matrix model, with Polyakov line as the unitary matrix, is an effective description of a QCD at finite density and temperature with $N$ number of colors and $N_f$ number of quark flavors defined on the manifold $S^1 \times S^3$. A distinct feature of this model, the occurrence of a series of Gross-Witten-Wadia transitions, as a function of the quark chemical potential, is reproduced using complex Langevin simulations. We simulate several other observables including Polyakov lines and quark number density, for large $N$ and $N_f$ and found excellent match with the analytic results.
We formulate ${\cal N} = 2^*$ supersymmetric Yang-Mills theory on a Euclidean spacetime lattice using the method of topological twisting. The lattice formulation preserves one scalar supersymmetry charge at finite lattice spacing. The lattice theory is also local, gauge invariant and free from doublers. We can use the lattice formulation of ${\cal N} = 2^*$ supersymmetric Yang-Mills to study finite temperature nonperturbative sectors of the theory and thus validate the gauge-gravity duality conjecture in a nonconformal theory.
We consider a chain of Abelian Klebanov-Tarnopolsky fermionic tensor models coupled through quartic nearest-neighbor interactions. We characterize the gauge-singlet spectrum for small chains ($L=2,3,4,5$) and observe that the spectral statistics exhibits strong evidences in favor of quasi-many body localization.
We examine the possibility of dynamical supersymmetry breaking in two-dimensional $\mathcal{N} = (2, 2)$ supersymmetric Yang-Mills theory. The theory is discretized on a Euclidean spacetime lattice using a supersymmetric lattice action. We compute the vacuum energy of the theory at finite temperature and take the zero temperature limit. Supersymmetry will be spontaneously broken in this theory if the measured ground state energy is non-zero. By performing simulations on a range of lattices up to $96 \times 96$ we are able to perform a careful extrapolation to the continuum limit for a wide range of temperatures. Subsequent extrapolations to the zero temperature limit yield an upper bound on the ground state energy density. We find the energy density to be statistically consistent with zero in agreement with the absence of dynamical supersymmetry breaking in this theory.
The ${\cal N} = 2^*$ Yang-Mills theory in four dimensions is a non-conformal theory that appears as a mass deformation of maximally supersymmetric ${\cal N} = 4$ Yang-Mills theory. This theory also takes part in the AdS/CFT correspondence and its gravity dual is type IIB supergravity on the Pilch-Warner background. The finite temperature properties of this theory have been studied recently in the literature. It has been argued that at large $N$ and strong coupling this theory exhibits no thermal phase transition at any non-zero temperature. The low temperature ${\cal N} = 2^*$ plasma can be compared to the QCD plasma. We provide a lattice construction of ${\cal N} = 2^*$ Yang-Mills on a hypercubic lattice starting from the ${\cal N} = 4$ gauge theory. The lattice construction is local, gauge-invariant, free from fermion doubling problem and preserves a part of the supersymmetry. This nonperturbative formulation of the theory can be used to provide a highly nontrivial check of the AdS/CFT correspondence in a non-conformal theory.
We report on the results of numerical simulations of 1+1 dimensional SU(N) Yang-Mills theory with maximal supersymmetry at finite temperature and compactified on a circle. For large N this system is thought to provide a dual description of the decoupling limit of N coincident D1-branes on a circle. It has been proposed that at large N there is a phase transition at strong coupling related to the Gregory-Laflamme (GL) phase transition in the holographic gravity dual. In a high temperature limit there was argued to be a deconfinement transition associated to the spatial Polyakov loop, and it has been proposed that this is the continuation of the strong coupling GL transition. Investigating the theory on the lattice for SU(3) and SU(4) and studying the time and space Polyakov loops we find evidence supporting this. In particular at strong coupling we see the transition has the parametric dependence on coupling predicted by gravity. We estimate the GL phase transition temperature from the lattice data which, interestingly, is not yet known directly in the gravity dual. Fine tuning in the lattice theory is avoided by the use of a lattice action with exact supersymmetry.