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.
14366436
Superconformal indices for orbifold Chern-Simons theories
We calculate the superconformal indices of recently discovered three-dimensional N = 4,5 Chern-Simons-matter theories and compare them with the corresponding indices of supergravity on AdS4 times orbifolds of S^7 in the large N and large k limit. We find perfect agreement for orbifolds without fixed locus, and argue that the agreement can continue to hold for orbifolds with fixed locus provided that the mass shifts of the twisted sector states are properly taken into account. We also discuss the index for the so-called "dual ABJM" proposal.
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.
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.
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.
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.
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.
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.
14989133
Three-Dimensional Gorenstein Singularities and SU(3) Modular Invariants
Using N=2 Landau-Ginzburg theories, we examine the recent conjectures relating the SU(3) WZW modular invariants, finite subgroups of SU(3) and Gorenstein singularities. All isolated three-dimensional Gorenstein singularities do not appear to be related to any known Landau-Ginzburg theories, but we present some curious observations which suggest that the SU(3)_n/SU(2)xU(1) Kazama-Suzuki model may be related to a deformed geometry of C^3/Z_{n+3}xZ_{n+3}. The toric resolution diagrams of those particular singularities are also seen to be classifying the diagonal modular invariants of the SU(3)_n as well as the SU(2)_{n+1} WZW models.
122705764
Phenomenology of the heavy B H in a littlest Higgs model
14893616
Z boson pair production at CERN LHC in a stabilized Randall-Sundrum scenario
We study the Z boson pair production at LHC in the Randall-Sundrum scenario with the Goldberger-Wise stabilization mechanism. It is shown that comprehensive account of the Kaluza-Klein graviton and radion effects is crucial to probe the model: The KK graviton effects enhance the cross section of $g g \to Z Z$ on the whole so that the resonance peak of the radion becomes easy to detect, whereas the RS effects on the $q\bar{q} \to Z Z$ process are rather insignificant. The $p_T$ and invariant-mass distributions are presented to study the dependence of the RS model parameters. The production of longitudinally polarized Z bosons, to which the SM contributions are suppressed, is mainly due to KK gravitons and the radion, providing one of the most robust methods to signal the RS effects. The $1 \sigma$ sensitivity bounds on $(\Lambda_\pi, m_\phi)$ with $k/M_{\rm Pl} =0.1$ are also obtained such that the effective weak scale $\Lambda_\pi$ of order 5 TeV can be experimentally probed.