scholarly journals PERTURBATIVE VACUA FROM IIB MATRIX MODEL

2008 ◽  
Vol 23 (14n15) ◽  
pp. 2279-2280
Author(s):  
HIKARU KAWAI ◽  
MATSUO SATO
Keyword(s):  
String Theory ◽  
Path Integral ◽  
Matrix Model ◽  
Moduli Space ◽  
Two Dimensional ◽  
Reduced Models ◽  
Yang Mills ◽  
Large N ◽  
Super Yang Mills Theory

It has not been clarified whether a matrix model can describe various vacua of string theory. In this talk, we show that the IIB matrix model includes type IIA string theory1. In the naive large N limit of the IIB matrix model, configurations consisting of simultaneously diagonalizable matrices form a moduli space, although the unique vacuum would be determined by complicated dynamics. This moduli space should correspond to a part of perturbatively stable vacua of string theory. Actually, one point on the moduli space represents type IIA string theory. Instead of integrating over the moduli space in the path-integral, we can consider each of the simultaneously diagonalizable configurations as a background and set the fluctuations of the diagonal elements to zero. Such procedure is known as quenching in the context of the large N reduced models. By quenching the diagonal elements of the matrices to an appropriate configuration, we show that the quenched IIB matrix model is equivalent to the two-dimensional large N [Formula: see text] super Yang-Mills theory on a cylinder. This theory is nothing but matrix string theory and is known to be equivalent to type IIA string theory. As a result, we find the manner to take the large N limit in the IIB matrix model.

scholarly journals STRING HAMILTONIAN FROM GENERALIZED YANG–MILLS GAUGE THEORY IN TWO DIMENSIONS

2004 ◽  
Vol 19 (02) ◽  
pp. 205-225 ◽  
Author(s):  
FLORIAN DUBATH ◽  
SIMONE LELLI ◽  
ANNA RISSONE
Keyword(s):  
Gauge Theory ◽  
String Theory ◽  
Space Time ◽  
Two Dimensions ◽  
Two Dimensional ◽  
Bosonic Field ◽  
Standard Case ◽  
Free Fermions ◽  
Yang Mills ◽  
Large N

Two-dimensional SU (N) Yang–Mills theory is known to be equivalent to a string theory, as found by Gross in the large N limit, using the 1/N expansion. Later it was found that even a generalized YM theory leads to a string theory of the Gross type. In the standard YM theory case, Douglas and others found the string Hamiltonian describing the propagation and the interactions of states made of strings winding on a cylindrical space–time. We address the problem of finding a similar Hamiltonian for the generalized YM theory. As in the standard case we start by writing the theory as a theory of free fermions. Performing a bosonization, we express the Hamiltonian in terms of the modes of a bosonic field, that are interpreted as in the standard case as creation and destruction operators for states of strings winding around the cylindrical space–time. The result is similar to the standard Hamiltonian, but with new kinds of interaction vertices.

scholarly journals Field Strength Correlators for Two-Dimensional Yang–Mills Theories Over Riemann Surfaces

1997 ◽  
Vol 12 (26) ◽  
pp. 4743-4768 ◽  
Author(s):  
João P. Nunes ◽  
Howard J. Schnitzer
Keyword(s):  
Phase Transitions ◽  
Field Strength ◽  
Critical Point ◽  
Path Integral ◽  
Correlation Functions ◽  
Riemann Surfaces ◽  
Two Dimensional ◽  
Yang Mills ◽  
Large N ◽  
Topological Obstructions

The path integral computation of field strength correlation functions for two-dimensional Yang–Mills theories over Riemann surfaces is studied. The calculation is carried out by Abelianization, which leads to correlators that are topological. They are nontrivial as a result of the topological obstructions to the Abelianization. It is shown in the large N limit on the sphere that the correlators undergo second order phase transitions at the critical point. Our results are applied to a computation of contractible Wilson loops.

scholarly journals Exact 1/N expansion of Wilson loop correlators in $$ \mathcal{N} $$ = 4 Super-Yang-Mills theory

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Wolfgang Mück
Keyword(s):  
Matrix Model ◽  
Wilson Loop ◽  
Model Solution ◽  
Wilson Loops ◽  
Combinatorial Formula ◽  
Expectation Value ◽  
Yang Mills ◽  
Hooft Coupling ◽  
The Matrix ◽  
Super Yang Mills Theory

Abstract Supersymmetric circular Wilson loops in $$ \mathcal{N} $$ N = 4 Super-Yang-Mills theory are discussed starting from their Gaussian matrix model representations. Previous results on the generating functions of Wilson loops are reviewed and extended to the more general case of two different loop contours, which is needed to discuss coincident loops with opposite orientations. A combinatorial formula representing the connected correlators of multiply wound Wilson loops in terms of the matrix model solution is derived. Two new results are obtained on the expectation value of the circular Wilson loop, the expansion of which into a series in 1/N and to all orders in the ’t Hooft coupling λ was derived by Drukker and Gross about twenty years ago. The connected correlators of two multiply wound Wilson loops with arbitrary winding numbers are calculated as a series in 1/N. The coefficient functions are derived not only as power series in λ, but also to all orders in λ by expressing them in terms of the coefficients of the Drukker and Gross series. This provides an efficient way to calculate the 1/N series, which can probably be generalized to higher-point correlators.

scholarly journals Divergent ⇒ complex amplitudes in two dimensional string theory

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
Ashoke Sen
Keyword(s):  
Scattering Amplitudes ◽  
String Theory ◽  
Matrix Model ◽  
Two Dimensional ◽  
Full Matrix ◽  
Instanton Contribution ◽  
The Matrix ◽  
Theory Result ◽  
The One ◽  
Remarkable Agreement

Abstract In a recent paper, Balthazar, Rodriguez and Yin found remarkable agreement between the one instanton contribution to the scattering amplitudes of two dimensional string theory and those in the matrix model to the first subleading order. The comparison was carried out numerically by analytically continuing the external energies to imaginary values, since for real energies the string theory result diverges. We use insights from string field theory to give finite expressions for the string theory amplitudes for real energies. We also show analytically that the imaginary parts of the string theory amplitudes computed this way reproduce the full matrix model results for general scattering amplitudes involving multiple closed strings.

scholarly journals THE HAGEDORN TRANSITION AND THE MATRIX MODEL FOR STRINGS

1998 ◽  
Vol 13 (26) ◽  
pp. 2085-2094 ◽  
Author(s):  
B. SATHIAPALAN
Keyword(s):  
Matrix Model ◽  
Light Cone ◽  
Degrees Of Freedom ◽  
Low Energy ◽  
Matrix Formalism ◽  
Yang Mills ◽  
Large N ◽  
The Matrix ◽  
The Continuum ◽  
String Worldsheet

We use the matrix formalism to investigate what happens to strings above the Hagedorn temperature. We show that is not a limiting temperature but a temperature at which the continuum string picture breaks down. We study a collection of N D-0-branes arranged to form a string having N units of light-cone momentum. We find that at high temperatures the favored phase is one where the string worldsheet has disappeared and the low-energy degrees of freedom consists of N2 massless particles ("gluons"). The nature of the transition is very similar to the deconfinement transition in large-N Yang–Mills theories.

scholarly journals Testing the holographic principle using lattice simulations

2018 ◽  
Vol 175 ◽  
pp. 08004 ◽  
Author(s):  
Raghav G. Jha ◽  
Simon Catterall ◽  
David Schaich ◽  
Toby Wiseman
Keyword(s):  
Phase Transition ◽  
Black Hole ◽  
Strong Coupling ◽  
Type Ii ◽  
Two Dimensional ◽  
Yang Mills ◽  
Large N ◽  
Gauge Gravity ◽  
Gravity Duality ◽  
Made In

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.

scholarly journals Generalized two-dimensional Yang-Mills theory is a matrix string theory

2000 ◽  
Vol 88 (1-3) ◽  
pp. 142-151 ◽  
Author(s):  
M. Billò ◽  
M. Caselle ◽  
A. D'Adda ◽  
P. Provero
Keyword(s):  
String Theory ◽  
Two Dimensional ◽  
Yang Mills
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