Aspects of non-abelian gauge dynamics in two-dimensional Script N = (2,2) theories

By K. Hori, David Tong. 2006

145 citations recorded by the source corpus.

We study various aspects of = (2,2) supersymmetric non-Abelian gauge theories in two dimensions, with applications to string vacua. We compute the Witten index of SU(k) SQCD with 0$>N>0 flavors with twisted masses; the result is presented as the solution to a simple combinatoric problem. We further claim that the infra-red fixed point of SU(k) gauge theory with N massless flavors is non-singular if (k,N) passes a related combinatoric criterion. These results are applied to the study of a class of U(k) linear sigma models which, in one phase, reduce to sigma models on Calabi-Yau manifolds in Grassmannians. We show that there are multiple singularities in the middle of the one-dimensional K?hler moduli space, in contrast to the Abelian models. This result precisely matches the complex structure singularities of the proposed mirrors. In one specific example, we study the physics in the other phase of the K?hler moduli space and find that it reduces to a sigma model for a second Calabi-Yau manifold which is not birationally equivalent to the first. This proves a mathematical conjecture of R?dland.

Subfields: Geometry and Topology, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/b370589306ac30b5c9c65d0709619d77460a55cb

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Citations in the corpus

Exact Kähler potential from gauge theory and mirror symmetry (2012, methodology): “Certain non-abelian GLSM’s for non-complete intersections have been constructed recently [20, 21, 22, 23], and the two-sphere partition function is a new exact method to study them.”
Exact results in D = 2 supersymmetric gauge theories (2012, unknown): “duality [17] in two dimensions by comparing the partition functions of putative dual theories in various limits and nding exact agreement. Seiberg duality in two dimensional N= (2;2) gauge theories 5 [18] relates theories with NF >Nfundamental chiral multiplets, trivial superpotential and gauge g”
The Pfaffian-Grassmannian derived equivalence (2006, result): “ctured for a while. Indeed, Rødland [8] argued, by comparing solutions to the Picard-Fuchs equation, that the families of X’s and of Y’s appear to have the same mirror family. Recently, Hori and Tong [4] gave a more detailed string theory argument supporting the same conclusion. If we denote by Z th”
Elliptic Genera of Two-Dimensional $${\mathcal{N} = 2}$$N=2 Gauge Theories with Rank-One Gauge Groups (2013, methodology): “This agreement is expected for odd N : the present computation and the computation in [24] can be continuously connected by a path in the space of the twisted masses and the flavor holonomy on the torus.”
Two-Sphere Partition Functions and Gromov–Witten Invariants (2012, methodology): “ld via ZS2(GLSM) = exp −K(CY3) . (6.1) We veriﬁed this for the quintic, corresponding to an abelian GLSM [15], and for Rødland’s Pfaﬃan Calabi–Yau threefold in P6, corresponding to a non-abelian GLSM [17,19]. Heartened by an exact matching with results known from mirror symmetry, we then studied a n”
F-theory on all toric hypersurface fibrations and its Higgs branches (2014, background): “6 There has been a lot of recent progress in systematically extending the set of Calabi-Yau 1For recent advances on Calabi-Yau manifolds constructed as determinantal and Pfaffian varieties, see [8,9].”