Small deformation of a simple N=2 superconformal theory

We study an interesting relevant deformation of the simplest interacting N=2 SCFT---the original Argyres-Douglas (AD) theory. We argue that, although this deformation is not strictly speaking Banks-Zaks like (certain operator dimensions change macroscopically), there are senses in which it constitutes a mild deformation of the parent AD theory: the exact change in the "a" anomaly is small and is essentially saturated at one loop. Moreover, contributions from IR operators that have a simple description in the UV theory reproduce a particular limit of the IR index to a remarkably high order. These results lead us to conclude that the IR theory is an interacting N=1 SCFT with particularly small "a" and "c" central charges and that this theory sheds some interesting light on the spectrum of its AD parent.The work of M. B. is partially supported by the Royal Society under the grant “New Constraints and Phenomena in Quantum Field Theory” and by the U.S. Department of Energy under Grant No. DE-SC0009924. T. N. is partially supported by the Yukawa Memorial Foundation

On Irregular Singularity Wave Functions and Superconformal Indices

We generalize, in a manifestly Weyl-invariant way, our previous expressions for irregu- lar singularity wave functions in two-dimensional SU(2) q-deformed Yang-Mills theory to SU(N). As an application, we give closed-form expressions for the Schur indices of all (AN−1,AN(n−1)−1) Argyres-Douglas (AD) superconformal field theories (SCFTs), thus com- pleting the computation of these quantities for the (AN , AM ) SCFTs. With minimal effort, our wave functions also give new Schur indices of various infinite sets of “Type IV” AD theories. We explore the discrete symmetries of these indices and also show how highly intricate renormalization group (RG) flows from isolated theories and conformal manifolds in the ultraviolet to isolated theories and (products of) conformal manifolds in the infrared are encoded in these indices. We compare our flows with dimensionally reduced flows via a simple “monopole vev RG” formalism. Finally, since our expressions are given in terms of concise Lie algebra data, we speculate on extensions of our results that might be useful for probing the existence of hypothetical SCFTs based on other Lie algebras. We conclude with a discussion of some open problems

N=2 S-Duality Revisited

Using the chiral algebra bootstrap, we revisit the simplest Argyres-Douglas (AD) generalization of Argyres-Seiberg S-duality. We argue that the exotic AD superconformal field theory (SCFT), T_{3, 3/2}, emerging in this duality splits into a free piece and an interacting piece, T_{X}, even though this factorization seems invisible in the Seiberg-Witten (SW) curve derived from the corresponding M5-brane construction. Without a Lagrangian, an associated topological field theory, a BPS spectrum, or even an SW curve, we nonetheless obtain exact information about TX by bootstrapping its chiral algebra, χ(T_{X}), and finding the corresponding vacuum character in terms of Affine Kac-Moody characters. By a standard 4D/2D correspondence, this result gives us the Schur index for T_{X} and, by studying this quantity in the limit of small S_{1}, we make contact with a proposed S_{1} reduction. Along the way, we discuss various properties of T_{X} : as an N = 1 theory, it has flavor symmetry SU(3) × SU(2) × U(1), the central charge of χ(T_{X}) matches the central charge of the bc ghosts in bosonic string theory, and its global SU(2) symmetry has a Witten anomaly. This anomaly does not prevent us from building conformal manifolds out of arbitrary numbers of T_{X} theories (giving us a surprisingly close AD relative of Gaiotto’s TN theories), but it does lead to some open questions in the context of the chiral algebra / 4D N = 2 SCFT correspondence

Evidence for Duality of Conifold from Fundamental String

We study the spectrum of BPS D5-D3-F1 states in type IIB theory, which are proposed to be dual to D4-D2-D0 states on the resolved conifold in type IIA theory. We evaluate the BPS partition functions for all values of the moduli parameter in the type IIB side, and find them completely agree with the results in the type IIA side which was obtained by using Kontsevich-Soibelman's wall-crossing formula. Our result is a quite strong evidence for string dualities on the conifold.Comment: 24 pages, 13 figures, v2: typos corrected, v3: explanations about wall-crossing improved and figures adde

Multiple D4-D2-D0 on the Conifold and Wall-crossing with the Flop

We study the wall-crossing phenomena of D4-D2-D0 bound states with two units of D4-brane charge on the resolved conifold. We identify the walls of marginal stability and evaluate the discrete changes of the BPS indices by using the Kontsevich-Soibelman wall-crossing formula. In particular, we find that the field theories on D4-branes in two large radius limits are properly connected by the wall-crossings involving the flop transition of the conifold. We also find that in one of the large radius limits there are stable bound states of two D4-D2-D0 fragments.Comment: 24 pages, 4 figures; v2: typos corrected, minor changes, a reference adde

Statistical model and BPS D4-D2-D0 counting

We construct a statistical model that correctly reproduces the BPS partition function of D4-D2-D0 bound states on the resolved conifold. We prove that the known partition function of the BPS indices is reproduced by the counting "triangular partitions" problem. The wall-crossing phenomena in our model are also studied.Comment: 9 pages, 6 figures; v2: typos corrected, minor change

Wall-crossing, open BPS counting and matrix models

We consider wall-crossing phenomena associated to the counting of D2-branes attached to D4-branes wrapping lagrangian cycles in Calabi-Yau manifolds, both from M-theory and matrix model perspective. Firstly, from M-theory viewpoint, we review that open BPS generating functions in various chambers are given by a restriction of the modulus square of the open topological string partition functions. Secondly, we show that these BPS generating functions can be identified with integrands of matrix models, which naturally arise in the free fermion formulation of corresponding crystal models. A parameter specifying a choice of an open BPS chamber has a natural, geometric interpretation in the crystal model. These results extend previously known relations between open topological string amplitudes and matrix models to include chamber dependence.Comment: 25 pages, 8 figures, published versio