A bstract When a quantum field theory is trivially gapped, its infrared fixed point an invertible theory. The partition function of the records response to various background fields in long-distance limit. set can include spacetime-dependent coupling constants, which case we call corresponding parameterized We study such theories arising from free Dirac fermions with mass parameters using Atiya...

We give a proof of the cobordism invariance of the index of elliptic pseudodifferential operators on σ-compact manifolds, where, in the non-compact case, the operators are assumed to be multiplication outside a compact set. We show that, if the principal symbol class of such an elliptic operator on the boundary of a manifold X has a suitable extension to K1(TX), then its index is zero. This con...

In this article, we survey the gluing formulae of the spectral invariants the ζ-regularized determinant of a Laplace type operator and the eta invariant of a Dirac type operator. After these spectral invariants had been originally introduced by Ray-Singer [30] and Atiyah-Patodi-Singer [1] respectively, these invariants have been studied by many people in many different parts of mathematics and ...

We consider the problem of automatic vocal melody transcription: translating an audio recording of a sung melody into a musical score. While previous work has focused on finding the closest notes to the singer’s tracked pitch, we instead seek to recover the melody the singer intended to sing. Often, the melody a singer intended to sing differs from what they actually sang; our hypothesis is tha...

where a, b, c, and d are real constants. These systems, derived by Bona, Saut and Toland for describing small-amplitude long waves in a water channel, are formally equivalent to the classical Boussinesq system and correct through first order with regard to a small parameter characterizing the typical amplitude-todepth ratio. Exact solutions for a large class of systems are presented. The existe...

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...