 Award ID(s):
 1720321
 NSFPAR ID:
 10147600
 Date Published:
 Journal Name:
 International Journal of Modern Physics A
 Volume:
 34
 Issue:
 30
 ISSN:
 0217751X
 Page Range / eLocation ID:
 1950181
 Format(s):
 Medium: X
 Sponsoring Org:
 National Science Foundation
More Like this

null (Ed.)A bstract In this note we study IR limits of pure twodimensional supersymmetric gauge theories with semisimple nonsimplyconnected gauge groups including SU( k )/ℤ k , SO(2 k )/ℤ 2 , Sp(2 k )/ℤ 2 , E 6 /ℤ 3 , and E 7 /ℤ 2 for various discrete theta angles, both directly in the gauge theory and also in nonabelian mirrors, extending a classification begun in previous work. We find in each case that there are supersymmetric vacua for precisely one value of the discrete theta angle, and no supersymmetric vacua for other values, hence supersymmetry is broken in the IR for most discrete theta angles. Furthermore, for the one distinguished value of the discrete theta angle for which supersymmetry is unbroken, the theory has as many twisted chiral multiplet degrees of freedom in the IR as the rank. We take this opportunity to further develop the technology of nonabelian mirrors to discuss how the mirror to a G gauge theory differs from the mirror to a G / K gauge theory for K a subgroup of the center of G . In particular, the discrete theta angles in these cases are considerably more intricate than those of the pure gauge theories studied in previous papers, so we discuss the realization of these more complex discrete theta angles in the mirror construction. We find that discrete theta angles, both in the original gauge theory and their mirrors, are intimately related to the description of centers of universal covering groups as quotients of weight lattices by root sublattices. We perform numerous consistency checks, comparing results against basic grouptheoretic relations as well as with decomposition, which describes how twodimensional theories with oneform symmetries (such as pure gauge theories with nontrivial centers) decompose into disjoint unions, in this case of pure gauge theories with quotiented gauge groups and discrete theta angles.more » « less

Abstract In this paper we propose a definition of torsion refined Gopakumar–Vafa (GV) invariants for Calabi–Yau threefolds with terminal nodal singularities that do not admit Kähler crepant resolutions. Physically, the refinement takes into account the charge of fivedimensional BPS states under a discrete gauge symmetry in Mtheory. We propose a mathematical definition of the invariants in terms of the geometry of all nonKähler crepant resolutions taken together. The invariants are encoded in the Amodel topological string partition functions associated to noncommutative (nc) resolutions of the Calabi–Yau. Our main example will be a singular degeneration of the generic Calabi–Yau double cover of
and leads to an enumerative interpretation of the topological string partition function of a hybrid Landau–Ginzburg model. Our results generalize a recent physical proposal made in the context of torus fibered Calabi–Yau manifolds by one of the authors and clarify the associated enumerative geometry.$${\mathbb {P}}^3$$ ${P}^{3}$ 
We describe the effect of the gravitational [Formula: see text]parameter on the behavior of the stretched horizon of a black hole in [Formula: see text]dimensions. The gravitational [Formula: see text]term is a total derivative, however, it affects the transport properties of the horizon. In particular, the horizon acquires a thirdorder parity violating, dimensionless transport coefficient which affects the way localized perturbations scramble on the horizon. In the context of the gauge/gravity duality, the [Formula: see text]term induces a nontrivial contact term in the energy–momentum tensor of a [Formula: see text]dimensional largeN gauge theory, which admits a dual gravity description. As a consequence, the dual gauge theory in the presence of the [Formula: see text]term acquires the same thirdorder parity violating transport coefficient.more » « less

Abstract For an invertible quasihomogeneouspolynomial 𝒘 {{\boldsymbol{w}}} we prove an allgenus mirror theoremrelating two cohomological field theories of Landau–Ginzburg type.On the B side it is the Saito–Givental theory for a specificchoice of a primitive form. On the A side, it is the matrix factorization CohFTfor the dual singularity 𝒘 T {{\boldsymbol{w}}^{T}} with the maximal diagonal symmetry group.more » « less

null (Ed.)A bstract We study O ( n )symmetric twodimensional conformal field theories (CFTs) for a continuous range of n below two. These CFTs describe the fixed point behavior of selfavoiding loops. There is a pair of known fixed points connected by an RG flow. When n is equal to two, which corresponds to the KosterlitzThouless critical theory, the fixed points collide. We find that for n generic these CFTs are logarithmic and contain negative norm states; in particular, the O ( n ) currents belong to a staggered logarithmic multiplet. Using a conformal bootstrap approach we trace how the negative norm states decouple at n = 2, restoring unitarity. The IR fixed point possesses a local relevant operator, singlet under all known global symmetries of the CFT, and, nevertheless, it can be reached by an RG flow without tuning. Besides, we observe logarithmic correlators in the closely related Potts model.more » « less