A path integral derivation of χy\chi_y-genus

The formula for the Hirzebruch $\chi_y$-genus of complex manifolds is a consequence of the Hirzebruch-Riemann-Roch formula. The classical index formulae for Todd genus, Euler number, and Signature correspond to the case when the complex variable $y=$ 0, -1, and 1 respectively. Here we give a {\it direct} derivation of this nice formula based on supersymmetric quantum mechanics.Comment: 5 page

Possible Origin of Fermion Chirality and Gut Structure From Extra Dimensions

The fundamental chiral nature of the observed quarks and leptons and the emergence of the gauge group itself are most puzzling aspects of the standard model. Starting from general considerations of topological properties of gauge field configurations in higher space-time dimensions, it is shown that the existence of non-trivial structures in ten dimensions would determine a class of models corresponding to a grand unified GUT structure with complex fermion representations with respect to $SU(3)_C \otimes SU(2)_L \otimes U(1)_Y$. The discussion is carried out within the framework of string theories with characteristic energy scales below the Planck mass. Avoidance of topological obstructions upon continuous deformation of field configurations leads to global chiral symmetry breaking of the underlying fundamental theory, imposes rigorous restrictions on the structure of the vacuum and space-time itself and determines uniquely the gauge structure and matter content.Comment: final version to appear in Phys. Rev.

New Implications of Lorentz Violation

In this proceedings, I summarize two recently discovered theoretical implications that Lorentz violation has on physical systems. First, I discuss new models for neutrino oscillations in which relatively simple combinations of Lorentz-violating parameters can mimic the major features of the current neutrino oscillation data. Second, I will present results on Yang-Mills instantons in Lorentz-violating background fields. An explicit solution is presented for unit winding number in SU(2).Comment: 8 pages, proceedings for 2003 Coral Gables Conference, Ft. Lauderdale, F

Multi-Periodic Coherent States and the WKB-Exactness

We construct the path integral formula in terms of ``multi-periodic'' coherent state as an extension of the Nielsen-Rohrlich formula for spin. We make an exact calculation of the formula and show that, when a parameter corresponding to the magnitude of spin becomes large, the leading order term of the expansion coincides with the exact result. We also give an explicit correspondence between the trace formula in the multi-periodic coherent state and the one in the ``generalized'' coherent state.Comment: 28 pages, late

Multi-Periodic Coherent States and the WKB-Exactness II ``Non-compact Case and Classical theories Revisited''

We show that the WKB approximation gives the exact result in the trace formula of ``$CQ^N$'', which is the non-compact counterpart of $CP^N$, in terms of the ``multi-periodic'' coherent state. We revisit the symplectic 2-forms on $CP^N$ and $CQ^N$ and, especially, construct that on $CQ^N$ with the unitary form. We also revisit the exact calculation of the classical patition functions of them.Comment: LaTeX, 29 page

The unified Skyrmion profiles and Static Properties of Nucleons

An unified approximated solution for symmetric Skyrmions was proposed for the SU(2) Skyrme model for baryon numbers up to 8,which take the hybrid form of a kink-like solution and that given by the instanton method. The Skyrmion profiles are examined by computing lowest soliton energy as well as the static properties of nucleons within the framework of collective quantization, with a good agreement with the exact numeric results. The comparisons with the previous computations as well as the experimental data are also given.Comment: 6 pages, 3 figures, 3 tables, Created by LaTex Syste

Brane-worlds and theta-vacua

Reductions from odd to even dimensionalities ($5\to 4$ or $3\to 2$), for which the effective low-energy theory contains chiral fermions, present us with a mismatch between ultraviolet and infrared anomalies. This applies to both local (gauge) and global currents; here we consider the latter case. We show that the mismatch can be explained by taking into account a change in the spectral asymmetry of the massive modes--an odd-dimensional analog of the phenomenon described by the Atiyah-Patodi-Singer theorem in even dimensionalities. The result has phenomenological implications: we present a scenario in which a QCD-like $\theta$-angle relaxes to zero on a certain (possibly, cosmological) timescale, despite the absence of any light axion-like particle.Comment: 44 pages, 4 figure

A Newman-Penrose Calculator for Instanton Metrics

We present a Maple11+GRTensorII based symbolic calculator for instanton metrics using Newman-Penrose formalism. Gravitational instantons are exact solutions of Einstein's vacuum field equations with Euclidean signature. The Newman-Penrose formalism, which supplies a toolbox for studying the exact solutions of Einstein's field equations, was adopted to the instanton case and our code translates it for the computational use.Comment: 13 pages. Matches the published version. The web page of the codes is changed as https://github.com/tbirkandan/NPInstanto

Instanton-Meron Hybrid in the Background of Gravitational Instantons

When it comes to the topological aspects, gravity may have profound effects even at the level of particle physics despite its negligibly small relative strength well below the Planck scale. In spite of this intriguing possibility, relatively little attempt has been made toward the exhibition of this phenomenon in relevant physical systems. In the present work, perhaps the simplest and the most straightforward new algorithm for generating solutions to (anti) self-dual Yang-Mills (YM) equation in the typical gravitational instanton backgrounds is proposed and then applied to find the solutions practically in all the gravitational instantons known. Solutions thus obtained turn out to be some kind of instanton-meron hybrids possessing mixed features of both. Namely, they are rather exotic type of configurations obeying first order (anti) self-dual YM equation which are everywhere non-singular and have finite Euclidean YM actions on one hand while exhibiting meron-like large distance behavior and carrying generally fractional topological charge values on the other. Close inspection, however, reveals that the solutions are more like instantons rather than merons in their generic natures.Comment: 33pages, Revtex, typos correcte