We investigate chiral zero modes and winding numbers at fixed points on ${T}^{2}/{\mathbb{Z}}_{N}$ orbifolds. It is shown that the Atiyah-Singer index theorem for leads to a formula ${n}_{+}\ensuremath{-}{n}_{\ensuremath{-}}=\phantom{\rule{0ex}{0ex}}(\ensuremath{-}{V}_{+}+{V}_{\ensuremath{-}})/2N$, where ${n}_{\ifmmode\pm\else\textpm\fi{}}$ are of $\ifmmode\pm\else\textpm\fi{}$ ${V}_{\ifmmode\p...

We investigate chiral zero modes and winding numbers at fixed points on ${T}^{2}/{\mathbb{Z}}_{N}$ orbifolds. It is shown that the Atiyah-Singer index theorem for leads to a formula ${n}_{+}\ensuremath{-}{n}_{\ensuremath{-}}=\phantom{\rule{0ex}{0ex}}(\ensuremath{-}{V}_{+}+{V}_{\ensuremath{-}})/2N$, where ${n}_{\ifmmode\pm\else\textpm\fi{}}$ are of $\ifmmode\pm\else\textpm\fi{}$ ${V}_{\ifmmode\p...

We use the Atiyah-Singer index theorem to derive general form of one-loop corrections observables in asymptotically anti-de Sitter (AdS$_4$) supersymmetric backgrounds abelian gauged supergravity. Using method supergravity localization combined with factorization action on fixed points (NUTs) and two-manifolds (Bolts) we show that an analogous takes place for determinants fields. This allows us...

We discuss the behaviour of the signature index class of closed foliated bundles under the operation of cutting and pasting. Along the way we establish several index theoretic results: we define Atiyah-Patodi-Singer (≡ APS) index classes for Dirac-type operators on foliated bundles with boundary; we prove a relative index theorem for the difference of two APS-index classes associated to differe...

Abstract. This paper is companion to our earlier work [8] (see also announcement [7]). Let M be a closed manifold and Y be an embedded hypersurface, such that there is a decomposition of M = M1 ∪M2 into two manifolds with boundary M1 and M2 , with M1 ∩M2 = Y . In [8] we proved the decomposition formula for detζ∆ the ζ-determinant of a Dirac Laplacian ∆ on M . The contributions coming from M1 an...

Gender identification application of Music Information Retrieval (MIR) research requires that the audio features that are extracted from the sound files should be sufficiently strong to be able to correctly classify the singer into male or a female. In literature, a lot of such applications are developed for speaker’s gender identification. Unfortunately, these applications cannot be applied fo...