Quantum vacua of 2d maximally supersymmetric YangMills theory
Abstract
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)^{D1}/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 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 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 {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 modularinvariant Abelian (multiperiodic and meromorphic) functions, which turns out to be very restrictive.
 Publication:

Journal of High Energy Physics
 Pub Date:
 November 2017
 DOI:
 10.1007/JHEP11(2017)140
 arXiv:
 arXiv:1609.08232
 Bibcode:
 2017JHEP...11..140K
 Keywords:

 Brane Dynamics in Gauge Theories;
 Dbranes;
 Sigma Models;
 Supersymmetric Gauge Theory;
 High Energy Physics  Theory
 EPrint:
 47 pages. Comments welcome!