R-Twisting and 4d/2d Correspondences

By S. Cecotti, Andrew Neitzke, C. Vafa. 2010

268 citations recorded by the source corpus.

We show how aspects of the R-charge of N=2 CFTs in four dimensions are encoded in the q-deformed Kontsevich-Soibelman monodromy operator, built from their dyon spectra. In particular, the monodromy operator should have finite order if the R-charges are rational. We verify this for a number of examples including those arising from pairs of ADE singularities on a Calabi-Yau threefold (some of which are dual to 6d (2,0) ADE theories suitably fibered over the plane). In these cases we find that our monodromy maps to that of the Y-systems, studied by Zamolodchikov in the context of TBA. Moreover we find that the trace of the (fractional) q-deformed KS monodromy is given by the characters of 2d conformal field theories associated to the corresponding TBA (i.e. integrable deformations of the generalized parafermionic systems). The Verlinde algebra gets realized through evaluation of line operators at the loci of the associated hyperKahler manifold fixed under R-symmetry action. Moreover, we propose how the TBA system arises as part of the N=2 theory in 4 dimensions. Finally, we initiate a classification of N=2 superconformal theories in 4 dimensions based on their quiver data and find that this classification problem is mapped to the classification of N=2 theories in 2 dimensions, and use this to classify all the 4d, N=2 theories with up to 3 generators for BPS states.

Subfields: Geometry and Topology, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/b855611c37487dbb2fae9af6fd74c42f2475ab18

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In Geometry and Topology

1. Dan Xie
2. C. Vafa
3. Mina Aganagic
4. L. Rastelli
5. Sergei Gukov
6. Sh. Shakirov
7. Abhijit Gadde
8. E. Witten

In Nuclear and High Energy Physics

1. L. Rastelli
2. Yuji Tachikawa
3. Ashoke Sen
4. Dan Xie
5. C. Vafa
6. D. Gaiotto
7. K. Maruyoshi
8. Abhijit Gadde

In Statistical and Nonlinear Physics

1. Ashoke Sen
2. Yuji Tachikawa
3. Dan Xie
4. C. Vafa
5. Mina Aganagic
6. B. Pioline
7. L. Rastelli
8. Abhijit Gadde

Citations in the corpus

• Gauge Theories and Macdonald Polynomials (2011, background): “or the non-Lagrangian SCFTs, which by denition are not continuously connected 1Though very large, class Sdoes not cover the full space of N= 2 SCFTs. Counterexamples can be found e.g. in [1, 3]. See [4, 3, 5] for the beginning of a classication program for N= 2 4dSCFTs. 2On the other hand, the confo”
• Schur indices, BPS particles, and Argyres-Douglas theories (2015, methodology): “Let us also clarify the relation of our operator O(q) to the BPS monodromy M(q) appearing in [19].”
• Classification of Complete N = 2 Supersymmetric Theories in 4 Dimensions (2011, methodology): “Hence, the only N = 2 theories with the properties that all quivers in their mutation classes have only single–lines are the ADE Argyres–Douglas ones (already studied in [2]).”
• Knot Homology from Refined Chern-Simons Theory (2011, methodology): “The light modes correspond to perturbative Chern-Simons gauge fields, while the heavy modes correspond to the open topological string instantons [53].”
• $\mathcal{N} = 2$ quantum field theories and their BPS quivers (2011, methodology): “We will consider the Argyres-Douglas A2 theory, whose quiver is given by two nodes connected by a single arrow [13].”
• Fivebranes and Knots (2011, background): “The six-dimensional starting point in the present section will also bring us closer to the brane constructions that have been used previously in related work [82], [53], [26], [2], and [19].”
• Wild quiver gauge theories (2011, background): “2 Gauge theories with strongly coupled sectors In [8] (see also [12]), a class of N = 2 gauge theories associated with a Riemann surface with higher order singularities was discussed.”
• N=2 Supersymmetric Dynamics for Pedestrians (2013, background): “This class of theories was introduced and studied in [81].”
• General Argyres-Douglas theory (2012, background): “and the common denominator of the scaling dimension is 8 which is in agreement with the result in [17].”
• Spectral Networks (2012, unknown): “(34)It was noted in [9, 21] that the K-transformations which appeared there could be viewed as cluster transformations in an appropriate sense; see also [10, 38, 48, 53, 54] for further discussion of the relation of cluster varieties to four-dimensional N = 2 theory.”
• Wall crossing from Boltzmann black hole halos (2010, background): “Since these two formulæ appeared, much efforts have been devoted towards interpreting, deriving and checking these wall-crossing formulæ in various physical settings [15, 16, 17, 18, 19, 20, 21, 22, 23].”