Goro Ishiki

N = 4 super Yang-Mills theory from the plane wave matrix model

We propose a nonperturbative definition of N=4 super Yang-Mills (SYM). We realize N=4 SYM on RxS{sup 3} as the theory around a vacuum of the plane wave matrix model. Our regularization preserves 16 supersymmetries and the gauge symmetry. We perform the 1-loop calculation to give evidences that the superconformal symmetry is restored in the continuum limit.

Deconfinement phase transition in N=4 super Yang-Mills theory on R x S3 from supersymmetric matrix quantum mechanics.

We test the recent claim that supersymmetric matrix quantum mechanics with mass deformation preserving maximal supersymmetry can be used to study N=4 super Yang-Mills theory on R x S{3} in the planar limit. When the mass parameter is large, we can integrate out all of the massive fluctuations around a particular classical solution, which corresponds to R x S{3}. The resulting effective theory for the gauge field moduli at finite temperature reproduces the deconfinement phase transition in N=4 super Yang-Mills theory on R x S{3} at weak coupling. This transition was speculated to be a continuation of the conjectured phase transition at strong coupling, which corresponds to the Hawking-Page transition based on the gauge-gravity duality. At strong coupling, one can study the target theory by the new simulation method for supersymmetric matrix quantum mechanics.

Holographic description of a quantum black hole on a computer

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.

Embedding of theories with SU(2|4) symmetry into the plane wave matrix model

We study theories with SU(2|4) symmetry, which include the plane wave matrix model, 2+1 SYM on R ? S2 and = 4 SYM on R ? S3/Zk. All these theories possess many vacua. From Lin-Maldacenas method which gives the gravity dual of each vacuum, it is predicted that the theory around each vacuum of 2+1 SYM on R ? S2 and = 4 SYM on R ? S3/Zk is embedded in the plane wave matrix model. We show this directly on the gauge theory side. We clearly reveal relationships among the spherical harmonics on S3, the monopole harmonics and the harmonics on fuzzy spheres. We extend the compactification (the T-duality) in matrix models a la Taylor to that on spheres.

= 4 SYM on R × S3 and theories with 16 supercharges

We study N=4 SYM on R x S^3 and theories with 16 supercharges arising as its consistent truncations. These theories include the plane wave matrix model, N=4 SYM on R x S^2 and N=4 SYM on R x S^3/Z_k, and their gravity duals were studied by Lin and Maldacena. We make a harmonic expansion of the original N=4 SYM on R x S^3 and obtain each of the truncated theories by keeping a part of the Kaluza-Klein modes. This enables us to analyze all the theories in a unified way. We explicitly construct some nontrivial vacua of N=4 SYM on R x S^2. We perform 1-loop analysis of the original and truncated theories. In particular, we examine states regarded as the integrable SO(6) spin chain and a time-dependent BPS solution, which is considered to correspond to the AdS giant graviton in the original theory.

Testing a novel large-N reduction for = 4 super Yang-Mills theory on R × S3

Recently a novel large-N reduction has been proposed as a maximally supersymmetric regularization of = 4 super Yang-Mills theory on R × S3 in the planar limit. This proposal, if it works, will enable us to study the theory non-perturbatively on a computer, and hence to test the AdS/CFT correspondence analogously to the recent works on the D0-brane system. We provide a nontrivial check of this proposal by performing explicit calculations in the large-N reduced model, which is nothing but the so-called plane wave matrix model, around a particular stable vacuum corresponding to R × S3. At finite temperature and at weak coupling, we reproduce precisely the deconfinement phase transition in the = 4 super Yang-Mills theory on R × S3. This phase transition is considered to continue to the strongly coupled regime, where it corresponds to the Hawking-Page transition on the AdS side. We also perform calculations around other stable vacua, and reproduce the phase transition in super Yang-Mills theory on the corresponding curved space-times such as R × S3/Zq and R × S2.

T-duality, fiber bundles and matrices

We extend the T-duality for gauge theory to that on curved space described as a nontrivial fiber bundle. We also present a new viewpoint concerning the consistent truncation and the T-duality for gauge theory and discuss the relation between the vacua on the total space and on the base space. As examples, we consider S3(/Zk), S5(/Zk) and the Heisenberg nilmanifold.

Precision lattice test of the gauge/gravity duality at large N

We perform a systematic, large-scale lattice simulation of D0-brane quantum mechanics. The large-

Direct test of the AdS/CFT correspondence by Monte Carlo studies of \( \mathcal{N}=4 \) super Yang-Mills theory

N

Matrix Geometry and Coherent States

and continuum limits of the gauge theory are taken for the first time at various temperatures