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.
119683460
From SO/Sp instantons to W-algebra blocks
We study instanton partition functions for $ \mathcal{N} = 2 $ superconformal Sp(1) and SO(4) gauge theories. We find that they agree with the corresponding U(2) instanton partitions functions only after a non-trivial mapping of the microscopic gauge couplings, since the instanton counting involves different renormalization schemes. Geometrically, this mapping relates the Gaiotto curves of the different realizations as double coverings. We then formulate an AGT-type correspondence between Sp(1)/SO(4) instanton partition functions and chiral blocks with an underlying $ \mathcal{W}\left( {2,2} \right) $-algebra symmetry. This form of the correspondence eliminates the need to divide out extra U(1) factors. Finally, to check this correspondence for linear quivers, we compute expressions for the Sp(1) × SO(4) half-bifundamental.
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.
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.
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.
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
16221979
POLARIZATION EFFECTS ON THE E+E- W+W- PROCESS WITH LARGE EXTRA DIMENSIONS
Abstract We study large extra dimension effects on the polarizations of the W pair and electron beam at the e + e − → W + W − process. It is shown that the measurements of the cross section for transversely polarized W pair with the right-handed electron beam remarkably enhance the possibilities to see the low scale quantum gravity effects. Higher Linear Collider bounds on the string scale in this model can be obtained by using the left-handed electron beam.
15426025
Large extra dimension effects on the spin configuration of the top quark pair at e + e − colliders
Large extra dimension effects on the spin configuration of the top quark pair at the ${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}t\overline{t}$ process are studied. It is shown that the TeV scale quantum gravity effects cause significant deviations from standard model (SM) predictions for the spin configuration in the off-diagonal basis: they lead to substantial cross sections of the like-spin states of the top quark pair, which vanish in the SM; they weaken the pure dominance of the processes, the up-down (down-up) spin states for the left-handed (right-handed) beam. In addition it is shown that the angular cut $\ensuremath{-}0.5l\mathrm{cos}\ensuremath{\theta}l0$ is very effective to determine the sign of the quantum gravity corrections.
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.