Masanori Hanada

Monte Carlo Studies of Supersymmetric Matrix Quantum Mechanics with Sixteen Supercharges at Finite Temperature

We present the first Monte Carlo results for supersymmetric matrix quantum mechanics with 16 supercharges at finite temperature. The recently proposed nonlattice simulation enables us to include the effects of fermionic matrices in a transparent and reliable manner. The internal energy nicely interpolates the weak coupling behavior obtained by the high temperature expansion, and the strong coupling behavior predicted from the dual black-hole geometry. The Polyakov line asymptotes at low temperature to a characteristic behavior for a deconfined theory, suggesting the absence of a phase transition. These results provide highly nontrivial evidence for the gauge-gravity duality.

Black Holes and Random Matrices

A bstractWe argue that the late time behavior of horizon fluctuations in large anti-de Sitter (AdS) black holes is governed by the random matrix dynamics characteristic of quantum chaotic systems. Our main tool is the Sachdev-Ye-Kitaev (SYK) model, which we use as a simple model of a black hole. We use an analytically continued partition function |Z(β + it)|2 as well as correlation functions as diagnostics. Using numerical techniques we establish random matrix behavior at late times. We determine the early time behavior exactly in a double scaling limit, giving us a plausible estimate for the crossover time to random matrix behavior. We use these ideas to formulate a conjecture about general large AdS black holes, like those dual to 4D super-Yang-Mills theory, giving a provisional estimate of the crossover time. We make some preliminary comments about challenges to understanding the late time dynamics from a bulk point of view.

Nonlattice Simulation for Supersymmetric Gauge Theories in One Dimension

Lattice simulation of supersymmetric gauge theories is not straightforward. In some cases the lack of manifest supersymmetry just necessitates cumbersome fine-tuning, but in the worse cases the chiral and/or Majorana nature of fermions makes it difficult to even formulate an appropriate lattice theory. We propose circumventing all these problems inherent in the lattice approach by adopting a nonlattice approach for one-dimensional supersymmetric gauge theories, which are important in the string or M theory context. In particular, our method can be used to investigate the gauge-gravity duality from first principles, and to simulate M theory based on the matrix theory conjecture.

Numerical studies of the ABJM theory for arbitrary N at arbitrary coupling constant

A bstractWe show that the ABJM theory, which is an

Two-Dimensional Lattice for Four-Dimensional = 4 Supersymmetric Yang-Mills

\mathcal{N} = {6}

Loops versus matrices: The Nonperturbative aspects of noncritical string

superconformal U(N) × U(N) Chern-Simons gauge theory, can be studied for arbitrary N at arbitrary coupling constant by applying a simple Monte Carlo method to the matrix model that can be derived from the theory by using the localization technique. This opens up the possibility of probing the quantum aspects of M-theory and testing the AdS4/CFT3 duality at the quantum level. Here we calculate the free energy, and confirm the N3/2 scaling in the M-theory limit predicted from the gravity side. We also find that our results nicely interpolate the analytical formulae proposed previously in the M-theory and type IIA regimes. Furthermore, we show that some results obtained by the Fermi gas approach can be clearly understood from the constant map contribution obtained by the genus expansion. The method can be easily generalized to the calculations of BPS operators and to other theories that reduce to matrix models.

Holographic description of a quantum black hole on a computer

We construct a lattice formulation of a mass-deformed two-dimensional N = (8, 8) super Yang-Mills theory with preserving two supercharges exactly. Gauge fields are represented by compact unitary link variables, and the exact supercharges on the lattice are nilpotent up to gauge transformations and SU(2)R rotations. Due to the mass deformation, the lattice model is free from the vacuum degeneracy problem, which was encountered in earlier approaches, and flat directions of scalar fields are stabilized giving discrete minima representing fuzzy S. Around the trivial minimum, quantum continuum theory is obtained with no tuning, which serves a nonperturbative construction of the IIA matrix string theory. Moreover, around the minimum of k-coincident fuzzy spheres, four-dimensional N = 4 U(k) super Yang-Mills theory with two commutative and two noncommutative directions emerges. In this theory, sixteen supersymmetries are broken by the mass deformation to two. Assuming the breaking is soft, we give a scenario leading to undeformed N = 4 super Yang-Mills on R without any fine tuning. As an evidence for the validity of the assumption, some computation of 1-loop radiative corrections is presented.

Describing Curved Spaces by Matrices

The nonperturbative aspects of string theory are explored for non-critical string in two distinct formulations, loop equations and matrix models. The effects corresponding to the D-brane in these formulations are especially investigated in detail. It is shown that matrix models can universally yield a definite value of the chemical potential for an instanton while loop equations cannot. This implies that it may not be possible to formulate string theory nonperturbatively solely in terms of closed strings.

Multi-matrix models and emergent geometry

Black holes have been predicted to radiate particles and eventually evaporate, which has led to the information loss paradox and implies that the fundamental laws of quantum mechanics may be violated. Superstring theory, a consistent theory of quantum gravity, provides a possible solution to the paradox if evaporating black holes can actually be described in terms of standard quantum mechanical systems, as conjectured from the theory. Here, we test this conjecture by calculating the mass of a black hole in the corresponding quantum mechanical system numerically. Our results agree well with the prediction from gravity theory, including the leading quantum gravity correction. Our ability to simulate black holes offers the potential to further explore the yet mysterious nature of quantum gravity through well-established quantum mechanics. Numerical simulations of an evaporating black hole are consistent with a quantum description of gravity [Also see Perspective by Maldacena] Confirming cosmic dual conjecture Quantum mechanics and gravity can seem to contradict each other. Superstring theory may provide a route to reconcile the two, thanks to the gauge/gravity duality conjecture, which allows the system to be described mathematically. However, this conjecture has yet to be formally confirmed. Hanada et al. (see the Perspective by Maldacena) performed a simulation of the dual gauge theory in the parameter regime that corresponds to a quantum black hole. Their results agree with a prediction for an evaporating black hole, including quantum gravity corrections, confirming that the dual gauge theory indeed provides a complete description of the quantum nature of the evaporating black hole. Science, this issue p. 882; see also p. 806.

Monte Carlo Studies of Matrix Theory Correlation Functions

It is shown that a covariant derivative on any d-dimensional manifold M can be mapped to a set of d operators acting on the space of functions defined on the principal Spin(d)-bundle over M. In other words, any d-dimensional manifold can be described in terms of d operators acting on an infinite-dimensional space. Therefore it is natural to introduce a new interpretation of matrix models in which matrices represent such operators. In this interpretation, the diffeomorphism, local Lorentz symmetry and their higher-spin analogues are included in the unitary symmetry of the matrix model. Furthermore, the Einstein equation is obtained from the equation of motion, if we take the standard form of the action, S = −tr [Aa, Ab][A a , A b ] � .