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.
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.
1563485
Quiver tails and N=1$$ \mathcal{N}=1 $$ SCFTs from M5-branes
A bstractWe study a class of four-dimensional N=1$$ \mathcal{N}=1 $$ superconformal field theories obtained by wrapping M5-branes on a Riemann surface with punctures. We identify fourdimensional UV descriptions of the SCFTs corresponding to curves with a class of punctures. The quiver tails appearing in these UV descriptions differ significantly from their N=2$$ \mathcal{N}=2 $$ counterpart. We find a new type of object that we call the ‘Fan’. We show how to construct new N=1$$ \mathcal{N}=1 $$ superconformal theories using the Fan. Various dual descriptions for these SCFTs can be identified with different colored pair-of-pants decompositions. For example, we find an N=1$$ \mathcal{N}=1 $$ analog of Argyres-Seiberg duality for the SU(N ) SQCD with 2N flavors. We also compute anomaly coefficients and superconformal indices for these theories and show that they are invariant under dualities.
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.
122705764
Phenomenology of the heavy B H in a littlest Higgs model
11525411
A Model for neutrino warm dark matter and neutrino oscillations
Abstract The muon- and tau-neutrinos with the mass in the keV range, which are allowed in a low reheating temperature cosmology, can compose the warm dark matter of the universe. A model of four light neutrinos including the keV scale ν μ and ν τ is studied, which combines the seesaw mechanism and the Abelian flavor symmetry. The atmospheric neutrino anomaly is due to the ν μ – ν τ oscillation. The solar neutrino problem is answered by the oscillation into the light sterile neutrino, where the SMA, LMA, and LOW–QVO solutions can be accommodated in our scenario.
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.
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.
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.