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Title: Comments on Worldsheet Theories Dual to Free Large N Gauge Theories

Abstract

We continue to investigate properties of the worldsheet conformal field theories (CFTs) which are conjectured to be dual to free large N gauge theories, using the mapping of Feynman diagrams to the worldsheet suggested in [1]. The modular invariance of these CFTs is shown to be built into the formalism. We show that correlation functions in these CFTs which are localized on subspaces of the moduli space may be interpreted as delta-function distributions, and that this can be consistent with a local worldsheet description given some constraints on the operator product expansion coefficients. We illustrate these features by a detailed analysis of a specific four-point function diagram. To reliably compute this correlator we use a novel perturbation scheme which involves an expansion in the large dimension of some operators.

Authors:
; ; ; ; ; ; ; ;
Publication Date:
Research Org.:
Stanford Linear Accelerator Center (SLAC)
Sponsoring Org.:
USDOE
OSTI Identifier:
901255
Report Number(s):
SLAC-PUB-12405
hep-th/0703141; TRN: US200714%%103
DOE Contract Number:
AC02-76SF00515
Resource Type:
Technical Report
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; CORRELATION FUNCTIONS; DELTA FUNCTION; DIMENSIONS; FEYNMAN DIAGRAM; FIELD THEORIES; OPERATOR PRODUCT EXPANSION; Theory-HEP,HEPTH

Citation Formats

Aharony, Ofer, /Weizmann Inst. /Stanford U., ITP /SLAC, David, Justin R., Gopakumar, Rajesh, /Harish-Chandra Res. Inst., Komargodski, Zohar, /Weizmann Inst., Razamat, Shlomo S., and /Technion. Comments on Worldsheet Theories Dual to Free Large N Gauge Theories. United States: N. p., 2007. Web. doi:10.2172/901255.
Aharony, Ofer, /Weizmann Inst. /Stanford U., ITP /SLAC, David, Justin R., Gopakumar, Rajesh, /Harish-Chandra Res. Inst., Komargodski, Zohar, /Weizmann Inst., Razamat, Shlomo S., & /Technion. Comments on Worldsheet Theories Dual to Free Large N Gauge Theories. United States. doi:10.2172/901255.
Aharony, Ofer, /Weizmann Inst. /Stanford U., ITP /SLAC, David, Justin R., Gopakumar, Rajesh, /Harish-Chandra Res. Inst., Komargodski, Zohar, /Weizmann Inst., Razamat, Shlomo S., and /Technion. Wed . "Comments on Worldsheet Theories Dual to Free Large N Gauge Theories". United States. doi:10.2172/901255. https://www.osti.gov/servlets/purl/901255.
@article{osti_901255,
title = {Comments on Worldsheet Theories Dual to Free Large N Gauge Theories},
author = {Aharony, Ofer and /Weizmann Inst. /Stanford U., ITP /SLAC and David, Justin R. and Gopakumar, Rajesh and /Harish-Chandra Res. Inst. and Komargodski, Zohar and /Weizmann Inst. and Razamat, Shlomo S. and /Technion},
abstractNote = {We continue to investigate properties of the worldsheet conformal field theories (CFTs) which are conjectured to be dual to free large N gauge theories, using the mapping of Feynman diagrams to the worldsheet suggested in [1]. The modular invariance of these CFTs is shown to be built into the formalism. We show that correlation functions in these CFTs which are localized on subspaces of the moduli space may be interpreted as delta-function distributions, and that this can be consistent with a local worldsheet description given some constraints on the operator product expansion coefficients. We illustrate these features by a detailed analysis of a specific four-point function diagram. To reliably compute this correlator we use a novel perturbation scheme which involves an expansion in the large dimension of some operators.},
doi = {10.2172/901255},
journal = {},
number = ,
volume = ,
place = {United States},
year = {Wed Mar 21 00:00:00 EDT 2007},
month = {Wed Mar 21 00:00:00 EDT 2007}
}

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  • We continue to investigate properties of the worldsheet conformal field theories (CFTs) which are conjectured to be dual to free large N gauge theories, using the mapping of Feynman diagrams to the worldsheet suggested in [R. Gopakumar, Phys. Rev. D 70, 025009 (2004); ibid.70, 025010 (2004); C. R. Physique 5, 1111 (2004); Phys. Rev. D 72, 066008 (2005)]. The modular invariance of these CFTs is shown to be built into the formalism. We show that correlation functions in these CFTs which are localized on subspaces of the moduli space may be interpreted as delta-function distributions, and that this can bemore » consistent with a local worldsheet description given some constraints on the operator product expansion coefficients. We illustrate these features by a detailed analysis of a specific four-point function diagram. To reliably compute this correlator, we use a novel perturbation scheme which involves an expansion in the large dimension of some operators.« less
  • We argue that weakly coupled 3+1 dimensional large N SU(N) gauge theories, with 't Hooft coupling {gamma}, compactified on a three-sphere of radius R, exhibit a novel second order phase transition at a temperature T{sub c} = C{radical}{gamma} R. The known constant C depends on the details of the gauge theory. The phase transition is characterized by a change in the eigenvalue distributions of the fields. Above the transition, the only eigenvalues which condense are those of the lowest Kaluza-Klein mode of the spatial gauge field Ai on the three-sphere. Below the transition the eigenvalues of the lowest Kaluza-Klein modemore » of an additional field condense. We discuss in particular the examples of pure Yang-Mills theory and of the N = 4 supersymmetric Yang-Mills theory.« less
  • The scale breaking ..lambda.. parameters of the Euclidean and Hamiltonian formulations of the lattice regulated O(N) and SU(N) x SU(N) spin systems in 1 + 1 dimensions were computed in terms of the ..lambda../sub PV/ parameter of the Pauli-Villars regulated continuum models. Using lattice perturbation theory, the renormalized mass gap has been determined in terms of ..lambda../sub PV/ for each model. These results are compared to analogous calculations in SU(N) gauge theories.
  • High temperture cluster expansions are derived for the free energy of vortices in SU(2) and Z2 lattice gauge theories in 3 and 4 dimensions. The expected behavior of the vortex free energy is verified. It obeys an area law behavior. The coefficient of the area is shown to be equal to the string tension between static quarks. Its expansion is calculated up to the 12th order. For SU(2) in 4 dimensions, the result is compared with Monte Carlo calculations of Creutz and is in good agreement at strong and intermediate coupling.
  • We construct anomaly-free nonsupersymmetric large {ital N} gauge theories from orientifolds of type IIB on {bold C}{sup 3}/{Gamma} orbifolds. In particular, massless as well as tachyonic one-loop tadpoles are canceled in these models. This is achieved by starting with N=1,2 supersymmetric orientifolds with a well defined world-sheet description and including discrete torsion (which breaks supersymmetry) in the orbifold action. In this way we obtain nontrivial nonchiral as well as anomaly-free chiral large {ital N} gauge theories. We point out certain subtleties arising in the chiral cases. Subject to certain assumptions, these theories are shown to have the property that computationmore » of any {ital M}-point correlation function in these theories reduces to the corresponding computation in the parent N=4 oriented theory. This generalizes the analogous results recently obtained in supersymmetric large {ital N} gauge theories from orientifolds, as well as in (non)supersymmetric large {ital N} gauge theories without orientifold planes. {copyright} {ital 1999} {ital The American Physical Society}« less