119279674
2d TQFT structure of the superconformal indices with outer-automorphism twists
A bstractWe study the superconformal indices of 4d theories coming from 6d $ \mathcal{N} $ = (2, 0) theory of type Γ on a Riemann surface, with the action of the outer-automorphism σ in the trace. We find that the indices are given by the partition function of a deformed 2d Yang-Mills on the Riemann surface with gauge group G which is S-dual to the subgroup of Γ fixed by σ. In the 2-parameter deformed version, we find that it is governed not by Macdonald polynomials of type G, but by Macdonald polynomials associated to twisted affine root systems.
118574920
The ABCDEFG of instantons and W-algebras
A bstractFor arbitrary gauge groups, we check at the one-instanton level that the Nekrasov partition function of pure $ \mathcal{N} = {2} $ super Yang-Mills is equal to the norm of a certain coherent state of the corresponding W-algebra. For non-simply-laced gauge groups, we confirm in particular that the coherent state is in the twisted sector of a simply-laced W-algebra.
41215949
Towards a 4d/2d correspondence for Sicilian quivers
We study the 4d/2d AGT correspondence between four-dimensional instanton counting and two-dimensional conformal blocks for generalized SU(2) quiver gauge theories coming from punctured Gaiotto curves of arbitrary genus. We propose a conformal block description that corresponds to the elementary SU(2) trifundamental half-hypermultiplet, and check it against Sp(1) − SO(4) instanton counting.
53724358
New N = 1 dualities from M5-branes and outer-automorphism twists
A bstractWe generalize recent construction of four-dimensional $ \mathcal{N} $ = 1 SCFT from wrapping six-dimensional $ \mathcal{N} $ = (2, 0) theory on a Riemann surface to the case of D-type with outer-automorphism twists. This construction allows us to build various dual theories for a class of $ \mathcal{N} $ = 1 quiver theories of SO-USp type. In particular, we find there are five dual frames to SO(2N)/USp(2N−2)/G2 gauge theories with (4N−4)/(4N)/8 fundamental flavors, where three of them being non-Lagrangian. We check the dualities by computing the anomaly coefficients and the superconformal indices. In the process we verify that the index of D4 theory on a certain three punctured sphere with $ {{\mathbb{Z}}_2} $ and $ {{\mathbb{Z}}_3} $ twist lines exhibits expected symmetry enhancement from G2 × USp(6) to E7.
122685044
4d/2d Correspondence: Instantons and W -algebras
In this thesis, we study the 4d/2d correspondence of Alday-Gaiotto-Tachikawa, which relates the class of 4-dimensional N=2 gauge theories (theories of class S) to a 2-dimensional conformal field theory. The 4d gauge theories are obtained by compactifying 6-dimensional N=(2, 0) theory of type A, D, E on a Riemann surface C. On the 2-dimensional side, we have Toda theory on the surface C with W-algebra symmetry, which is an extension of the Virasoro symmetry. In particular, the instanton partition function of the 4d gauge theory is reproduced by a conformal/chiral block of Virasoro/W-algebra. We develop techniques to compute the partition functions on 4d and 2d sides, for various gauge groups and matter fields. We generalize the Alday-Gaiotto-Tachikawa 4d/2d correspondence to various cases. First, we study N=2 pure Yang-Mills theory with arbitrary gauge groups, including the exceptional groups. We explicitly construct the corresponding W-algebra currents, and confirm the correspondence holds at 1-instanton level. Second, we study the conformal quiver theory with Sp(1)-SO(4) gauge group. Finally, we study Sicilian gauge theories with trifundamental half-hypermultiplets. We also find that the conformal theories with Sp(1) gauge group and SU(2) gauge group have different instanton partition functions in terms of bare gauge couplings. We show this is an artifact of the renormalization scheme, by explicitly constructing a map between the bare couplings and studying its geometrical interpretations. This demonstrates the scheme independence of renormalization at the non-perturbative level.
26660560
Counting exceptional instantons
A bstractWe show how to obtain the instanton partition function of N = 2 SYM with exceptional gauge group EFG using blow-up recursion relations derived by Nakajima and Yoshioka. We compute the two instanton contribution and match it with the recent proposal for the superconformal index of rank 2 SCFTs with E6,7 global symmetry.
14815248
Phenomenological study of lepton mass matrix textures
The three active light neutrinos are used to explain the neutrino oscillations. The inherently bi-large mixing neutrino mass matrix and the Fritzsch type, bi-small mixing charged lepton mass matrix are assumed. By requiring the maximal �µ −�� mixing for the atmospheric neutrino problem and the masssquared difference approperiate for the almost maximal mixing solution to
119481975
Kaluza-Klein gravitino production with a single photon at e + e − colliders
In a supersymmetric large extra dimension scenario, the production of Kaluza-Klein gravitinos accompanied by a photino at ${e}^{+}{e}^{\ensuremath{-}}$ colliders is studied. We assume that a bulk supersymmetry is softly broken on our brane such that the low-energy theory resembles the MSSM. Low energy supersymmetry breaking is further assumed as in GMSB, leading to a sub-eV mass shift in each KK mode of the gravitino from the corresponding graviton KK mode. Since the photino decays within a detector due to the sufficiently large inclusive decay rate of $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\ensuremath{\gamma}}\ensuremath{\rightarrow}\ensuremath{\gamma}\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{G},$ the process ${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\ensuremath{\gamma}}\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{G}$ yields single photon events with missing energy. Even if the total cross section can be substantial at $\sqrt{s}=500\mathrm{GeV},$ the KK graviton background of ${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}\ensuremath{\gamma}G$ is kinematically advantageous and thus much larger. It is shown that the observable $\ensuremath{\Delta}{\ensuremath{\sigma}}_{\mathrm{LR}}\ensuremath{\equiv}\ensuremath{\sigma}{(e}_{L}^{\ensuremath{-}}{e}_{R}^{+})\ensuremath{-}\ensuremath{\sigma}{(e}_{R}^{\ensuremath{-}}{e}_{L}^{+})$ can completely eliminate the KK graviton background but retain most of the KK gravitino signal, which provides a unique and robust method to probe the supersymmetric bulk.
509681
Of McKay correspondence, non-linear sigma-model and conformal field theory
The ubiquitous ADE classification has induced many proposals of often mysterious correspondences both in mathematics and physics. The mathematics side includes quiver theory and the McKay Correspondence which relates finite group representation theory to Lie algebras as well as crepant resolutions of Gorenstein singularities. On the physics side, we have the graph-theoretic classification of the modular invariants of WZW models, as well as the relation between the string theory nonlinear $\sigma$-models and Landau-Ginzburg orbifolds. We here propose a unification scheme which naturally incorporates all these correspondences of the ADE type in two complex dimensions. An intricate web of inter-relations is constructed, providing a possible guideline to establish new directions of research or alternate pathways to the standing problems in higher dimensions.
16854157
Descendant Gromov-Witten Invariants, Simple Hurwitz Numbers, and the Virasoro Conjecture for P^1
In this ``experimental'' research, we use known topological recursion relations in genera-zero, -one, and -two to compute the n-point descendant Gromov-Witten invariants of P^1 for arbitrary degrees and low values of n. The results are consistent with the Virasoro conjecture and also lead to explicit computations of all Hodge integrals in these genera. We also derive new recursion relations for simple Hurwitz numbers similar to those of Graber and Pandharipande.
18394237
The Hurwitz Enumeration Problem of Branched Covers and Hodge Integrals
We use algebraic methods to compute the simple Hurwitz numbers for arbitrary source and target Riemann surfaces. For an elliptic curve target, we reproduce the results previously obtained by string theorists. Motivated by the Gromov-Witten potentials, we find a general generating function for the simple Hurwitz numbers in terms of the representation theory of the symmetric group S{sub n}. We also find a generating function for Hodge integrals on the moduli space {bar M}{sub g,2} of Riemann surfaces with two marked points, similar to that found by Faber and Pandharipande for the case of one marked point.