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.
15149403
Notes from the Underground: A Propos of Givental's Conjecture
These brief notes record our puzzles and findings surrounding Givental's recent conjecture which expresses higher genus Gromov-Witten invariants in terms of the genus-0 data. We limit our considerations to the case of a projective line, whose Gromov-Witten invariants are well-known and easy to compute. We make some simple checks supporting his conjecture.
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.
11586065
Scenario of light sterile neutrinos with a heavy tau neutrino in a supersymmetric model
Three light sterile neutrinos (nu (s)(e), nu (s)(mu) and nu (s)(tau)) are introduced to accommodate all the available neutrino data: the atmospheric neutrino anomaly is explained by nu (mu)-nu (s)(mu) oscillation with maximal mixing; the solar one is due to nu (e)-nu (s)(e) oscillation of small angle Mikheyev-Smirnov-Wolfenstein type; the Liquid Scintillation Neutrino Detector data is from v(e)-v(mu) oscillations, so that the neutrinos can be the hot component of the dark matter. The big bang nucleosynthesis constraint is satisfied by taking the tau neutrino to be 10 MeV heavy. The nu (tau) decay is discussed in a model of gauge mediated supersymmetry breaking. The decay mode v(tau) --> (G) over tilde gamma with (G) over tilde being the gravitino is proposed. The nu (tau) has a rather long lifetime similar to 10(3)-10(13) s. Its implication to the gamma-ray burst is discussed. (C) 2001 Elsevier Science B.V. All rights reserved.
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.
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.
119422313
Spin configuration of top quark pair production with large extra dimensions at photon-photon colliders
Top quark pair production at photon-photon colliders is studied in low scale quantum gravity scenario. From the dependence of the cross sections on the spin configuration of the top quark and anti-quark, we introduce a new observable, top spin asymmetry. It is shown that there exists a special top spin basis where with the polarized parent electron beams the top spin asymmetry vanishes in the standard model but retains substantial values with the large extra dimension effects. We also present lower bounds of the quantum gravity scale $M_S$ from total cross sections with various combinations of the laser, electron beam, and top quark pair polarizations. The measurements of the top spin state $(t_\uparrow\bar{t}_\downarrow)$ with unpolarized initial beams are shown to be most effective, enhancing by about 5% the $M_S$ bounds with respect to totally unpolarized case.