E8 gauge theory and gerbes in string theory

Research output: Contribution to journalArticle

Abstract

The reduction of the E8 gauge theory to ten dimensions leads to a loop group, which in relation to twisted K-theory has a Dixmier-Douady class identified with the Neveu-Schwarz H-field. We give an interpretation of the degree two part of the eta form by comparing the adiabatic limit of the eta invariant with the one loop term in type IIA. More generally, starting with a G-bundle, the comparison for manifolds with String structure identifies G with E8 and the representation as the adjoint, due to an interesting appearance of the dual Coxeter number. This makes possible a description in terms of a generalized Wess-Zumino-Witten model at the critical level. We also discuss the relation to the index gerbe, the possibility of obtaining such bundles from loop space, and the symmetry breaking to finite-dimensional bundles. We discuss the implications of this and we give several proposals.

Original languageEnglish (US)
Pages (from-to)399-438
Number of pages40
JournalAdvances in Theoretical and Mathematical Physics
Volume14
Issue number2
DOIs
StatePublished - Jan 1 2010

Fingerprint

Gerbes
String Theory
Gauge Theory
string theory
bundles
gauge theory
Bundle
Gerbe
G-structures
Eta Invariant
Loop Groups
Loop Space
K-theory
Symmetry Breaking
proposals
broken symmetry
strings
Strings
Term
Model

ASJC Scopus subject areas

  • Mathematics(all)
  • Physics and Astronomy(all)

Cite this

E8 gauge theory and gerbes in string theory. / Sati, Hisham.

In: Advances in Theoretical and Mathematical Physics, Vol. 14, No. 2, 01.01.2010, p. 399-438.

Research output: Contribution to journalArticle

@article{3462ff904fae435d836e540aae333a1f,
title = "E8 gauge theory and gerbes in string theory",
abstract = "The reduction of the E8 gauge theory to ten dimensions leads to a loop group, which in relation to twisted K-theory has a Dixmier-Douady class identified with the Neveu-Schwarz H-field. We give an interpretation of the degree two part of the eta form by comparing the adiabatic limit of the eta invariant with the one loop term in type IIA. More generally, starting with a G-bundle, the comparison for manifolds with String structure identifies G with E8 and the representation as the adjoint, due to an interesting appearance of the dual Coxeter number. This makes possible a description in terms of a generalized Wess-Zumino-Witten model at the critical level. We also discuss the relation to the index gerbe, the possibility of obtaining such bundles from loop space, and the symmetry breaking to finite-dimensional bundles. We discuss the implications of this and we give several proposals.",
author = "Hisham Sati",
year = "2010",
month = "1",
day = "1",
doi = "10.4310/ATMP.2010.v14.n2.a2",
language = "English (US)",
volume = "14",
pages = "399--438",
journal = "Advances in Theoretical and Mathematical Physics",
issn = "1095-0761",
publisher = "International Press of Boston, Inc.",
number = "2",

}

TY - JOUR

T1 - E8 gauge theory and gerbes in string theory

AU - Sati, Hisham

PY - 2010/1/1

Y1 - 2010/1/1

N2 - The reduction of the E8 gauge theory to ten dimensions leads to a loop group, which in relation to twisted K-theory has a Dixmier-Douady class identified with the Neveu-Schwarz H-field. We give an interpretation of the degree two part of the eta form by comparing the adiabatic limit of the eta invariant with the one loop term in type IIA. More generally, starting with a G-bundle, the comparison for manifolds with String structure identifies G with E8 and the representation as the adjoint, due to an interesting appearance of the dual Coxeter number. This makes possible a description in terms of a generalized Wess-Zumino-Witten model at the critical level. We also discuss the relation to the index gerbe, the possibility of obtaining such bundles from loop space, and the symmetry breaking to finite-dimensional bundles. We discuss the implications of this and we give several proposals.

AB - The reduction of the E8 gauge theory to ten dimensions leads to a loop group, which in relation to twisted K-theory has a Dixmier-Douady class identified with the Neveu-Schwarz H-field. We give an interpretation of the degree two part of the eta form by comparing the adiabatic limit of the eta invariant with the one loop term in type IIA. More generally, starting with a G-bundle, the comparison for manifolds with String structure identifies G with E8 and the representation as the adjoint, due to an interesting appearance of the dual Coxeter number. This makes possible a description in terms of a generalized Wess-Zumino-Witten model at the critical level. We also discuss the relation to the index gerbe, the possibility of obtaining such bundles from loop space, and the symmetry breaking to finite-dimensional bundles. We discuss the implications of this and we give several proposals.

UR - http://www.scopus.com/inward/record.url?scp=77957710516&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77957710516&partnerID=8YFLogxK

U2 - 10.4310/ATMP.2010.v14.n2.a2

DO - 10.4310/ATMP.2010.v14.n2.a2

M3 - Article

AN - SCOPUS:77957710516

VL - 14

SP - 399

EP - 438

JO - Advances in Theoretical and Mathematical Physics

JF - Advances in Theoretical and Mathematical Physics

SN - 1095-0761

IS - 2

ER -