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Quantum Vacua of 2d Maximally Supersymmetric Yang-Mills Theory

Koloğlu, Murat (2017) Quantum Vacua of 2d Maximally Supersymmetric Yang-Mills Theory. Journal of High Energy Physics, 2017 (11). Art. No. 140. ISSN 1126-6708. https://resolver.caltech.edu/CaltechAUTHORS:20161024-195243827

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Abstract

We analyze the classical and quantum vacua of 2d N=(8,8) supersymmetric Yang-Mills theory with SU(N) and U(N) gauge group, describing the worldvolume interactions of Nparallel D1-branes with flat transverse directions R^8. We claim that the IR limit of the SU(N) theory in the superselection sector labeled M (mod N) — identified with the internal dynamics of (M, N)-string bound states of the Type IIB string theory — is described by the symmetric orbifold N=(8,8) sigma model into (R^8)^(D−1)/S_D when D = gcd(M, N) > 1, and by a single massive vacuum when D = 1, generalizing the conjectures of E. Witten and others. The full worldvolume theory of the D1-branes is the U(N) theory with an additional U(1) 2-form gauge field B coming from the string theory Kalb-Ramond field. This U(N) + B theory has generalized field configurations, labeled by the Z-valued generalized electric flux and an independent Z_N-valued ’t Hooft flux. We argue that in the quantum mechanical theory, the (M, N)-string sector with M units of electric flux has a Z_N-valued discrete θ angle specified by M (mod N) dual to the ’t Hooft flux. Adding the brane center-of-mass degrees of freedom to the SU(N) theory, we claim that the IR limit of the U(N) + B theory in the sector with M bound F-strings is described by the N=(8,8) sigma model into Sym^D(R^8). We provide strong evidence for these claims by computing an N=(8,8) analog of the elliptic genus of the UV gauge theories and of their conjectured IR limit sigma models, and showing they agree. Agreement is established by noting that the elliptic genera are modular-invariant Abelian (multi-periodic and meromorphic) functions, which turns out to be very restrictive.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1007/JHEP11(2017)140DOIArticle
http://arxiv.org/abs/1609.08232arXivDiscussion Paper
ORCID:
AuthorORCID
Koloğlu, Murat0000-0002-5082-8434
Additional Information:© 2017 The Author(s). This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited. Received: June 23, 2017; Accepted: October 24, 2017; Published: November 22, 2017. The author would like to thank Sergei Gukov for suggesting this problem, and for his guidance. The author would also like to thank Abhijit Gadde and Du Pei for valuable discussions, and especially Ingmar Saberi for discussions and comments on a draft of this work. This material is based upon work supported by the U.S. Department of Energy, Office of Science, Office of High Energy Physics, under Award Number DE-SC0011632.
Group:Walter Burke Institute for Theoretical Physics
Funders:
Funding AgencyGrant Number
Department of Energy (DOE)DE-SC0011632
Subject Keywords:Brane Dynamics in Gauge Theories; D-branes; Sigma Models Supersymmetric Gauge Theory
Other Numbering System:
Other Numbering System NameOther Numbering System ID
CALT-TH2016-028
Issue or Number:11
Record Number:CaltechAUTHORS:20161024-195243827
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20161024-195243827
Official Citation:Koloğlu, M. J. High Energ. Phys. (2017) 2017: 140. https://doi.org/10.1007/JHEP11(2017)140
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:71432
Collection:CaltechAUTHORS
Deposited By: Joy Painter
Deposited On:25 Oct 2016 16:38
Last Modified:20 Nov 2020 19:20

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