Testing the holographic principle using lattice simulations

The lattice studies of maximally supersymmetric Yang-Mills (MSYM) theory at strong coupling and large N is important for verifying gauge/gravity duality. Due to the progress made in the last decade, based on ideas from topological twisting and orbifolding, it is now possible to study these theories on the lattice while preserving an exact supersymmetry on the lattice. We present some results from the lattice studies of two-dimensional MSYM which is related to Type II supergravity. Our results agree with the thermodynamics of different black hole phases on the gravity side and the phase transition (Gregory–Laflamme) between them.

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Gauge/gravity duality — From lattice gauge theory to black hole

International Journal of Modern Physics A ◽

10.1142/s0217751x17470182 ◽

2017 ◽

Vol 32 (36) ◽

pp. 1747018 ◽

Cited By ~ 1

Author(s):

Daisuke Kadoh

Keyword(s):

Black Hole ◽

Gauge Theory ◽

Finite Temperature ◽

Lattice Gauge Theory ◽

Yang Mills ◽

Lattice Gauge ◽

Large N ◽

Gauge Gravity ◽

Gravity Duality

The duality conjecture states that [Formula: see text]-dimensional maximally supersymmetric Yang–Mills theory at finite temperature is expected to be dual to the non extremal black [Formula: see text]-brane at large N. We perform the lattice simulations of SYM for [Formula: see text] to investigate the validity of the conjecture. We show that the conjecture is qualitatively valid by comparing lattice results of the black [Formula: see text]-branes mass with analytic expectations in the gravity side.

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A DIRECT TEST OF THE GAUGE/GRAVITY DUALITY AND THE STRING THEORETICAL DESCRIPTION OF A BLACK HOLE

International Journal of Modern Physics A ◽

10.1142/s0217751x08040706 ◽

2008 ◽

Vol 23 (14n15) ◽

pp. 2161-2164 ◽

Cited By ~ 1

Author(s):

JUN NISHIMURA

Keyword(s):

Black Hole ◽

Theoretical Description ◽

Direct Test ◽

Strongly Coupled ◽

Open Strings ◽

Large N ◽

Brane Solution ◽

Gauge Gravity ◽

Gravity Duality ◽

Microscopic Origin

We perform a direct test of the gauge/gravity duality by studying one-dimensional U (N) gauge theory with 16 supercharges at finite temperature using Monte Carlo simulation. In the 't Hooft large-N limit and in the strong coupling limit, the model is expected to have a dual gravity description in terms of the near-extremal black 0-brane solution in ten-dimensional type IIA supergravity. Our results provide the first example, in which the microscopic origin of the black hole thermodynamics is accounted for by solving explicitly the strongly coupled dynamics of the open strings attached to the D-branes.

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Non-hermitian holography

SciPost Physics ◽

10.21468/scipostphys.9.3.032 ◽

2020 ◽

Vol 9 (3) ◽

Author(s):

Daniel Arean ◽

Karl Landsteiner ◽

Ignacio Salazar Landea

Keyword(s):

Phase Transition ◽

Black Hole ◽

Quantum Theory ◽

Finite Temperature ◽

Similarity Transformation ◽

Zero Temperature ◽

Gauge Gravity ◽

Gravity Duality ◽

Linear Involution ◽

Black Hole Solutions

Quantum theory can be formulated with certain non-Hermitian Hamiltonians. An anti-linear involution, denoted by PT, is a symmetry of such Hamiltonians. In the PT-symmetric regime the non-Hermitian Hamiltonian is related to a Hermitian one by a Hermitian similarity transformation. We extend the concept of non-Hermitian quantum theory to gauge-gravity duality. Non-Hermiticity is introduced via boundary conditions in asymptotically AdS spacetimes. At zero temperature the PT phase transition is identified as the point at which the solutions cease to be real. Surprisingly at finite temperature real black hole solutions can be found well outside the quasi-Hermitian regime. These backgrounds are however unstable to fluctuations which establishes the persistence of the holographic dual of the PT phase transition at finite temperature.

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MORE ON GENERALIZED SIMPLICIAL CHIRAL MODELS

International Journal of Modern Physics A ◽

10.1142/s0217751x01003172 ◽

2001 ◽

Vol 16 (06) ◽

pp. 1161-1171

Author(s):

M. ALIMOHAMMADI ◽

KH. SAAIDI

Keyword(s):

Phase Transition ◽

Partition Function ◽

Density Function ◽

Path Integration ◽

Two Dimensional ◽

Third Order ◽

Dimensional Simplex ◽

Yang Mills ◽

Eigenvalue Density ◽

Large N

By generalizing the auxiliary field term in the Lagrangian of simplicial chiral models on a (d-1)-dimensional simplex, the generalized simplicial chiral models has been introduced in Ref. 1. These models can be solved analytically only in d=0 and d=2 cases at large-N limit. In the d=0 case, we calculate the eigenvalue density function in strong regime and show that the partition function computed from this density function is consistent with one calculated by path integration directly. In the d=2 case, it is shown that all V= Tr (AA†)n models have a third order phase transition, the same as the two-dimensional Yang–Mills theory.

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MULTI-INSTANTON EFFECT IN TWO-DIMENSIONAL QCD

Modern Physics Letters A ◽

10.1142/s0217732395001678 ◽

1995 ◽

Vol 10 (21) ◽

pp. 1549-1563

Author(s):

TETSUYUKI OCHIAI

Keyword(s):

Phase Transition ◽

Integral Representation ◽

Interaction Effect ◽

Contour Integral ◽

Two Dimensional ◽

Free Energies ◽

Yang Mills ◽

Large N ◽

Instanton Effect

We analyze multi-instanton sector in two-dimensional U(N) Yang-Mills theory on a sphere. We obtain a contour integral representation of the multi-instanton amplitude and find “neutral” configurations of the even number instantons dominate in the large-N limit. Using this representation, we calculate the 1-, 2-, 3-, 4-body interactions and the free energies for N=3, 4, 5 numerically and find that the multi-instanton interaction effect essentially contributes to the large-N phase transition discovered by Douglas and Kazakov.

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Black Hole Solution of Einstein-Born-Infeld-Yang-Mills Theory

Advances in High Energy Physics ◽

10.1155/2017/2038202 ◽

2017 ◽

Vol 2017 ◽

pp. 1-7 ◽

Cited By ~ 1

Author(s):

Kun Meng ◽

Da-Bao Yang ◽

Zhan-Ning Hu

Keyword(s):

Phase Transition ◽

Black Hole ◽

Phase Space ◽

Cosmological Constant ◽

Black Hole Solution ◽

Extended Phase Space ◽

Extended Phase ◽

Yang Mills ◽

First Law Of Thermodynamics ◽

Dimensional Black Hole

A new four-dimensional black hole solution of Einstein-Born-Infeld-Yang-Mills theory is constructed; several degenerated forms of the black hole solution are presented. The related thermodynamical quantities are calculated, with which the first law of thermodynamics is checked to be satisfied. Identifying the cosmological constant as pressure of the system, the phase transition behaviors of the black hole in the extended phase space are studied.

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