Quantum vacua of 2d maximally supersymmetric YangMills theory
Abstract
Here, we analyze the classical and quantum vacua of 2d N = (8,8) supersymmetric YangMills theory with SU(N) and U(N) gauge group, describing the worldvolume interactions of N parallel D1branes 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/SD 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 world volume theory of the D1branes is the U(N) theory with an additional U(1) 2form gauge field B coming from the string theory KalbRamond field. This U(N) + B theory has generalized field configurations, labeled by the Zvalued 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 centerofmass degrees ofmore »
 Authors:

 California Inst. of Technology (CalTech), Pasadena, CA (United States). Walter Burke Inst. for Theoretical Physics
 Publication Date:
 Research Org.:
 California Inst. of Technology, Pasadena, CA (United States)
 Sponsoring Org.:
 USDOE Office of Science (SC), High Energy Physics (HEP)
 OSTI Identifier:
 1501470
 Grant/Contract Number:
 SC0011632
 Resource Type:
 Accepted Manuscript
 Journal Name:
 Journal of High Energy Physics (Online)
 Additional Journal Information:
 Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2017; Journal Issue: 11; Journal ID: ISSN 10298479
 Publisher:
 Springer Berlin
 Country of Publication:
 United States
 Language:
 English
 Subject:
 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Brane Dynamics in Gauge Theories; Dbranes; Sigma Models; Supersymmetric Gauge Theory
Citation Formats
Koloğlu, Murat. Quantum vacua of 2d maximally supersymmetric YangMills theory. United States: N. p., 2017.
Web. doi:10.1007/jhep11(2017)140.
Koloğlu, Murat. Quantum vacua of 2d maximally supersymmetric YangMills theory. United States. doi:10.1007/jhep11(2017)140.
Koloğlu, Murat. Wed .
"Quantum vacua of 2d maximally supersymmetric YangMills theory". United States. doi:10.1007/jhep11(2017)140. https://www.osti.gov/servlets/purl/1501470.
@article{osti_1501470,
title = {Quantum vacua of 2d maximally supersymmetric YangMills theory},
author = {Koloğlu, Murat},
abstractNote = {Here, we analyze the classical and quantum vacua of 2d N = (8,8) supersymmetric YangMills theory with SU(N) and U(N) gauge group, describing the worldvolume interactions of N parallel D1branes with flat transverse directions R8. 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 (R8)D–1/SD 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 world volume theory of the D1branes is the U(N) theory with an additional U(1) 2form gauge field B coming from the string theory KalbRamond field. This U(N) + B theory has generalized field configurations, labeled by the Zvalued generalized electric flux and an independent ZNvalued ’t Hooft flux. We argue that in the quantum mechanical theory, the (M, N)string sector with M units of electric flux has a ZNvalued discrete θ angle specified by M (mod N) dual to the ’t Hooft flux. Adding the brane centerofmass 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 Fstrings is described by the N = (8,8) sigma model into SymD(R8). 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 modularinvariant Abelian (multiperiodic and meromorphic) functions, which turns out to be very restrictive.},
doi = {10.1007/jhep11(2017)140},
journal = {Journal of High Energy Physics (Online)},
number = 11,
volume = 2017,
place = {United States},
year = {2017},
month = {11}
}
Web of Science
Works referenced in this record:
Elliptic Genera of 2d $${\mathcal{N}}$$ N = 2 Gauge Theories
journal, November 2014
 Benini, Francesco; Eager, Richard; Hori, Kentaro
 Communications in Mathematical Physics, Vol. 333, Issue 3
A new supersymmetric index
journal, November 1992
 Cecotti, Sergio; Fendley, Paul; Intriligator, Ken
 Nuclear Physics B, Vol. 386, Issue 2
Supersymmetric YangMills theories
journal, March 1977
 Brink, Lars; Schwarz, John H.; Scherk, J.
 Nuclear Physics B, Vol. 121, Issue 1
From 0branes to torons
journal, June 1998
 Guralnik, Z.; Ramgoolam, S.
 Nuclear Physics B, Vol. 521, Issue 12
DLCQ spectrum of $\mathcal{N}=(8,8)\mathrm{}$ super YangMills theory
journal, October 1998
 Antonuccio, F.; Lunin, O.; Pinsky, S.
 Physical Review D, Vol. 58, Issue 10
Elliptic genera and quantum field theory
journal, December 1987
 Witten, Edward
 Communications in Mathematical Physics, Vol. 109, Issue 4
2d index and surface operators
journal, March 2014
 Gadde, Abhijit; Gukov, Sergei
 Journal of High Energy Physics, Vol. 2014, Issue 3
Notes on theories with 16 supercharges
journal, July 1998
 Seiberg, Nathan
 Nuclear Physics B  Proceedings Supplements, Vol. 67, Issue 13
Sevensphere and the exceptional N = 7 and N = 8 superconformal algebras
journal, May 1996
 Günaydin, Murat; Ketov, Sergei V.
 Nuclear Physics B, Vol. 467, Issue 12
On the LandauGinzburg Description of n=2 Minimal Models
journal, October 1994
 Witten, Edward
 International Journal of Modern Physics A, Vol. 09, Issue 27
Torons and Dbrane bound states
journal, August 1997
 Guralnik, Z.; Ramgoolam, S.
 Nuclear Physics B, Vol. 499, Issue 12
Two dimensional gauge theories revisited
journal, October 1992
 Witten, Edward
 Journal of Geometry and Physics, Vol. 9, Issue 4
Automorphic forms onO s +2,2(R) and infinite products
journal, December 1995
 Borcherds, Richard E.
 Inventiones Mathematicae, Vol. 120, Issue 1
Matrix string theory
journal, September 1997
 Dijkgraaf, Robbert; Verlinde, Erik; Verlinde, Herman
 Nuclear Physics B, Vol. 500, Issue 13
Lowenergy spectrum of Script N = 4 superYangMills on T ^{3} : flat connections, bound states at threshold, and S duality
journal, June 2007
 Henningson, Måns; Wyllard, Niclas
 Journal of High Energy Physics, Vol. 2007, Issue 06
On moduli spaces of flat connections with nonsimply connected structure group
journal, May 1997
 Schweigert, Christoph
 Nuclear Physics B, Vol. 492, Issue 3
Bound states of strings and pbranes
journal, February 1996
 Witten, Edward
 Nuclear Physics B, Vol. 460, Issue 2
The YangMills Equations over Riemann Surfaces
journal, March 1983
 Atiyah, M. F.; Bott, R.
 Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 308, Issue 1505
Elliptic Genera of TwoDimensional $${\mathcal{N} = 2}$$ N = 2 Gauge Theories with RankOne Gauge Groups
journal, November 2013
 Benini, Francesco; Eager, Richard; Hori, Kentaro
 Letters in Mathematical Physics, Vol. 104, Issue 4
Dbranes in a topologically nontrivial $B$field
journal, January 2000
 Kapustin, Anton
 Advances in Theoretical and Mathematical Physics, Vol. 4, Issue 1
$\theta $ angle monodromy in two dimensions
journal, May 2012
 Lawrence, Albion
 Physical Review D, Vol. 85, Issue 10
On the Algebras of BPS States
journal, October 1998
 Harvey, Jeffrey A.; Moore, Gregory
 Communications in Mathematical Physics, Vol. 197, Issue 3
Elliptic Genera of Symmetric Products and Second Quantized Strings
journal, April 1997
 Dijkgraaf, Robbert; Moore, Gregory; Verlinde, Erik
 Communications in Mathematical Physics, Vol. 185, Issue 1
Coupling a QFT to a TQFT and duality
journal, April 2014
 Kapustin, Anton; Seiberg, Nathan
 Journal of High Energy Physics, Vol. 2014, Issue 4
Supersymmetries and their representations
journal, March 1978
 Nahm, W.
 Nuclear Physics B, Vol. 135, Issue 1
θvacua in twodimensional quantum chromodynamics
journal, June 1979
 Witten, E.
 Il Nuovo Cimento A, Vol. 51, Issue 3
(0, 2) trialities
journal, March 2014
 Gadde, Abhijit; Gukov, Sergei; Putrov, Pavel
 Journal of High Energy Physics, Vol. 2014, Issue 3
Reading between the lines of fourdimensional gauge theories
journal, August 2013
 Aharony, Ofer; Seiberg, Nathan; Tachikawa, Yuji
 Journal of High Energy Physics, Vol. 2013, Issue 8
Some computations for m dimensional partitions
journal, October 1967
 Atkin, A. O. L.; Bratley, P.; Macdonald, I. G.
 Mathematical Proceedings of the Cambridge Philosophical Society, Vol. 63, Issue 4
Works referencing / citing this record:
Holomorphic field theories and Calabi–Yau algebras
journal, June 2019
 Eager, Richard; Saberi, Ingmar
 International Journal of Modern Physics A, Vol. 34, Issue 16
Holomorphic field theories and Calabi–Yau algebras
journal, June 2019
 Eager, Richard; Saberi, Ingmar
 International Journal of Modern Physics A, Vol. 34, Issue 16
Spherical branes
journal, August 2018
 Bobev, Nikolay; Bomans, Pieter; Gautason, Fridrik Freyr
 Journal of High Energy Physics, Vol. 2018, Issue 8