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Title: World Sheet Commuting beta-gamma CFT and Non-Relativistic StringTheories

Abstract

We construct a sigma model in two dimensions with Galilean symmetry in flat target space similar to the sigma model of the critical string theory with Lorentz symmetry in 10 flat spacetime dimensions. This is motivated by the works of Gomis and Ooguri[1] and Danielsson et. al.[2, 3]. Our theory is much simpler than their theory and does not assume a compact coordinate. This non-relativistic string theory has a bosonic matter {beta}{gamma} CFT with the conformal weight of {beta} as 1. It is natural to identify time as a linear combination of {gamma} and {bar {gamma}} through an explicit realization of the Galilean boost symmetry. The angle between {gamma} and {bar {gamma}} parametrizes one parameter family of selection sectors. These selection sectors are responsible for having a non-relativistic dispersion relation without a nontrivial topology in the non-relativistic setup, which is one of the major differences from the previous works[1, 2, 3]. This simple theory is the non-relativistic analogue of the critical string theory, and there are many different avenues ahead to be investigated. We mention a possible consistent generalization of this theory with different conformal weights for the {beta}{gamma} CFT. We also mention supersymmetric generalizations of these theories.

Authors:
Publication Date:
Research Org.:
Ernest Orlando Lawrence Berkeley NationalLaboratory, Berkeley, CA (US)
Sponsoring Org.:
USDOE
OSTI Identifier:
927836
Report Number(s):
LBNL-63372; UCB-PTH-07/15, arXiv:0708.4261
TRN: US0804731
DOE Contract Number:
DE-AC02-05CH11231
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physical Review D; Journal Volume: 76; Related Information: Journal Publication Date: 2007
Country of Publication:
United States
Language:
English
Subject:
72; DIMENSIONS; DISPERSION RELATIONS; SIGMA MODEL; SPACE-TIME; SYMMETRY; TARGETS; TOPOLOGY

Citation Formats

Kim, Bom Soo. World Sheet Commuting beta-gamma CFT and Non-Relativistic StringTheories. United States: N. p., 2007. Web.
Kim, Bom Soo. World Sheet Commuting beta-gamma CFT and Non-Relativistic StringTheories. United States.
Kim, Bom Soo. Thu . "World Sheet Commuting beta-gamma CFT and Non-Relativistic StringTheories". United States. doi:. https://www.osti.gov/servlets/purl/927836.
@article{osti_927836,
title = {World Sheet Commuting beta-gamma CFT and Non-Relativistic StringTheories},
author = {Kim, Bom Soo},
abstractNote = {We construct a sigma model in two dimensions with Galilean symmetry in flat target space similar to the sigma model of the critical string theory with Lorentz symmetry in 10 flat spacetime dimensions. This is motivated by the works of Gomis and Ooguri[1] and Danielsson et. al.[2, 3]. Our theory is much simpler than their theory and does not assume a compact coordinate. This non-relativistic string theory has a bosonic matter {beta}{gamma} CFT with the conformal weight of {beta} as 1. It is natural to identify time as a linear combination of {gamma} and {bar {gamma}} through an explicit realization of the Galilean boost symmetry. The angle between {gamma} and {bar {gamma}} parametrizes one parameter family of selection sectors. These selection sectors are responsible for having a non-relativistic dispersion relation without a nontrivial topology in the non-relativistic setup, which is one of the major differences from the previous works[1, 2, 3]. This simple theory is the non-relativistic analogue of the critical string theory, and there are many different avenues ahead to be investigated. We mention a possible consistent generalization of this theory with different conformal weights for the {beta}{gamma} CFT. We also mention supersymmetric generalizations of these theories.},
doi = {},
journal = {Physical Review D},
number = ,
volume = 76,
place = {United States},
year = {Thu Aug 30 00:00:00 EDT 2007},
month = {Thu Aug 30 00:00:00 EDT 2007}
}
  • We construct a sigma model in two dimensions with Galilean symmetry in flat target space similar to the sigma model of the critical string theory with Lorentz symmetry in 10 flat spacetime dimensions. This is motivated by the works of Gomis and Ooguri [J. Math. Phys. (N.Y.) 42, 3127 (2001)] and Danielsson et al. [J. High Energy Phys. 10 (2000) 020; J. High Energy Phys. 03 (2001) 041.]. Our theory is much simpler than their theory and does not assume a compact coordinate. This nonrelativistic string theory has a bosonic matter {beta}{gamma} conformal field theory with the conformal weight ofmore » {beta} as 1. It is natural to identify time as a linear combination of {gamma} and {gamma} through an explicit realization of the Galilean boost symmetry. The angle between {gamma} and {gamma} parametrizes one parameter family of selection sectors. These selection sectors are responsible for having a nonrelativistic dispersion relation without a nontrivial topology in the nonrelativistic setup, which is one of the major differences from the previous works of Gomis and Ooguri and of Danielsson and co-workers. This simple theory is the nonrelativistic analogue of the critical string theory, and there are many different avenues ahead to be investigated. We mention a possible consistent generalization of this theory with different conformal weights for the {beta}{gamma} conformal field theory. We also mention supersymmetric generalizations of these theories.« less
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  • We consider non-Abelian 1/2 Bogomol'nyi-Prasad-Sommerfield (BPS) flux tubes (strings) in a deformed N=2 supersymmetric gauge theory, with mass terms {mu}{sub 1,2} of the adjoint fields breaking N=2 down to N=1. The main feature of the non-Abelian strings is the occurrence of orientational moduli associated with the possibility of rotations of their color fluxes inside a global SU(N) group. The bulk four-dimensional theory has four supercharges; half-criticality of the non-Abelian strings would imply then N=1 supersymmetry on the world sheet, i.e. two supercharges. In fact, superalgebra of the reduced moduli space has four supercharges. Internal dynamics of the orientational moduli aremore » described by a two-dimensional CP(N-1) model on the string world sheet. We focus mainly on the SU(2) case, i.e. CP(1) world-sheet theory. We show that non-Abelian BPS strings exist for all values of {mu}{sub 1,2}. The low-energy theory of moduli is indeed CP(1), with four supercharges, in a wide region of breaking parameters {mu}{sub 1,2}. Only in the limit of very large {mu}{sub 1,2}, above some critical value does the N=2 world-sheet supersymmetry break down to N=1. We observe 'supersymmetry emergence' for the flux-tube junction (confined monopole): The kink-monopole is half-critical considered from the standpoint of the world-sheet CP(1) model (i.e. two supercharges conserved), while in the bulk N=1 theory there is no monopole central charge at all.« less
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