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.
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.
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.
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.
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.
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.
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.
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