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 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 THEORETICAL INTERPRETATION FOR FINITE N YANG–MILLS THEORY IN TWO DIMENSIONS

2005 ◽  
Vol 20 (01) ◽  
pp. 29-41 ◽  
Author(s):  
TOSHIHIRO MATSUO ◽  
SO MATSUURA
Keyword(s):  
Asymptotic Expansion ◽  
Closed String ◽  
Two Dimensions ◽  
Perturbative Expansion ◽  
Target Space ◽  
Theoretical Interpretation ◽  
Two Dimensional ◽  
Yang Mills ◽  
Large N ◽  
Residual Part

We discuss the equivalence between a string theory and the two-dimensional Yang–Mills theory with SU (N) gauge group for finite N. We find a sector which can be interpreted as a sum of covering maps from closed string worldsheets to the target space, whose covering number is less than N. This gives an asymptotic expansion of 1/N whose large N limit becomes the chiral sector defined by Gross and Taylor. We also discuss that the residual part of the partition function provides the nonperturbative corrections to the perturbative expansion.

QUANTIZATION OF THE LIOUVILLE MODE AND STRING THEORY

1989 ◽  
Vol 04 (11) ◽  
pp. 1033-1041 ◽  
Author(s):  
SUMIT R. DAS ◽  
SATCHIDANANDA NAIK ◽  
SPENTA R. WADIA
Keyword(s):  
String Theory ◽  
Dimensional Space ◽  
Scalar Fields ◽  
Space Time ◽  
Two Dimensions ◽  
General Covariance ◽  
World Sheet ◽  
Lorentzian Signature ◽  
Dimensional Space Time ◽  
Background Fields

We discuss the space-time interpretation of bosonic string theories, which involve d scalar fields coupled to gravity in two dimensions, with a proper quantization of the world-sheet metric. We show that for d>25, the theory cannot describe string modes consistently coupled to each other. For d=25 this is possible; however, in this case the Liouville mode acts as an extra timelike variable and one really has a string moving in 26-dimensional space-time with a Lorentzian signature. By analyzing such a string theory in background fields, we show that the d=25 theory possesses the full 26-dimensional general covariance.

scholarly journals HIGHER GAUGE THEORY AND GRAVITY IN 2+1 DIMENSIONS

2007 ◽  
Vol 22 (28) ◽  
pp. 5155-5172 ◽  
Author(s):  
R. B. MANN ◽  
E. M. POPESCU
Keyword(s):  
Gauge Theory ◽  
Two Dimensional ◽  
Yang Mills ◽  
Higher Dimensional ◽  
Present Context ◽  
Dimensional Gravity ◽  
Wide Perspective ◽  
Higher Gauge Theory ◽  
Matter Fields ◽  
New Framework

Non-Abelian higher gauge theory has recently emerged as a generalization of standard gauge theory to higher-dimensional (two-dimensional in the present context) connection forms, and as such, it has been successfully applied to the non-Abelian generalizations of the Yang–Mills theory and 2-form electrodynamics. (2+1)-dimensional gravity, on the other hand, has been a fertile testing ground for many concepts related to classical and quantum gravity, and it is therefore only natural to investigate whether we can find an application of higher gauge theory in this latter context. In the present paper we investigate the possibility of applying the formalism of higher gauge theory to gravity in 2+1 dimensions, and we show that a nontrivial model of (2+1)-dimensional gravity coupled to scalar and tensorial matter fields — the ΣΦEA model — can be formulated as a higher gauge theory (as well as a standard gauge theory). Since the model has a very rich structure — it admits as solutions black-hole BTZ-like geometries, particle-like geometries as well as Robertson–Friedman–Walker cosmological-like expanding geometries — this opens a wide perspective for higher gauge theory to be tested and understood in a relevant gravitational context. Additionally, it offers the possibility of studying gravity in 2+1 dimensions coupled to matter in an entirely new framework.

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 ARITHMETIC SPACE–TIME GEOMETRY FROM STRING THEORY

2006 ◽  
Vol 21 (31) ◽  
pp. 6323-6350 ◽  
Author(s):  
ROLF SCHIMMRIGK
Keyword(s):  
Field Theory ◽  
String Theory ◽  
Modular Forms ◽  
Complex Multiplication ◽  
Space Time ◽  
Two Dimensional ◽  
Conformal Field ◽  
Exactly Solvable

An arithmetic framework for string compactification is described. The approach is exemplified by formulating a strategy that allows to construct geometric compactifications from exactly solvable theories at c = 3. It is shown that the conformal field theoretic characters can be derived from the geometry of space–time, and that the geometry is uniquely determined by the two-dimensional field theory on the worldsheet. The modular forms that appear in these constructions admit complex multiplication, and allow an interpretation as generalized McKay–Thompson series associated to the Mathieu and Conway groups. This leads to a string motivated notion of arithmetic moonshine.

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

scholarly journals A TOY MODEL OF CLOSED STRING TACHYON EFFECTIVE ACTION

2005 ◽  
Vol 20 (07) ◽  
pp. 1481-1493
Author(s):  
J. KLUSOŇ
Keyword(s):  
Exact Solution ◽  
String Theory ◽  
Effective Action ◽  
Flat Space ◽  
Closed String ◽  
Space Time ◽  
Bosonic String ◽  
Two Dimensional ◽  
Linear Dilaton ◽  
Bosonic String Theory

In this paper we propose the toy model of the closed string tachyon effective action that has marginal tachyon profile as its exact solution in case of constant or linear dilaton background. Then we will apply this model for description of two-dimensional bosonic string theory. We will find that the background configuration with the spatial dependent linear dilaton, flat space–time metric and marginal tachyon profile is the exact solution of our model even if we take into account backreaction of tachyon on dilaton and on metric.

Beta functions in Chirally deformed supersymmetric sigma models in two dimensions

2016 ◽  
Vol 31 (28n29) ◽  
pp. 1645040
Author(s):  
Arkady Vainshtein
Keyword(s):  
Sigma Models ◽  
Two Dimensions ◽  
Two Dimensional ◽  
World Sheet ◽  
Yang Mills ◽  
Anomalous Dimensions ◽  
Straightforward Method ◽  
The World ◽  
Original Formula

We study two-dimensional sigma models where the chiral deformation diminished the original [Formula: see text] supersymmetry to the chiral one, [Formula: see text]. Such heterotic models were discovered previously on the world sheet of non-Abelian stringy solitons supported by certain four-dimensional [Formula: see text] theories. We study geometric aspects and holomorphic properties of these models, and derive a number of exact expressions for the [Formula: see text] functions in terms of the anomalous dimensions analogous to the NSVZ [Formula: see text] function in four-dimensional Yang-Mills. Instanton calculus provides a straightforward method for the derivation.

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