Related papers: Warped Schwarzian theory
We develop a formulation of perturbation theory on spherically symmetric backgrounds based on self-dual curvature equations combined with spherical harmonic expansions. The resulting framework unifies the Regge-Wheeler-Zerilli (RWZ) and…
We study the spectral properties of the Laplace operator associated to a hyperbolic surface in the presence of a unitary representation of the fundamental group. Following the approach by Guillop\'e and Zworski, we establish a factorization…
We study perturbative Wilsonian renormalisation group (RG) for the scalar $\phi^4$ theory at finite temperature to one loop order in the Schwinger-Keldysh closed-time-path (CTP) formalism. By explicitly integrating out the UV modes, we show…
The Virasoro operations in Witten's theory of two-dimensional topological gravity have a homotopy-theoretic interpretation as endomorphisms of an ordinary cohomology theory with coefficients in a localization of I. Schur's ring \Delta of…
We propose the superintegrable generalization of Smorodinsky-Winternitz system on the $N$-dimensional complex Euclidian space which is specified by the presence of constant magnetic field. We find out that in addition to $2N$ Liouville…
We discuss the general form of the mass terms that can appear in the effective field theories of coordinate-dependent compactifications a la Scherk-Schwarz. As an illustrative example, we consider an interacting five-dimensional theory…
We introduce and study wheeled PROPs, an extension of the theory of PROPs which can treat traces and, in particular, solutions to the master equations which involve divergence operators. We construct a dg free wheeled PROP whose…
The algebra dual to Woronowicz's deformation of the 2-\-di\-men\-sion\-al Euclidean group is constructed. The same algebra is obtained from $SU_{q}(2)$ via contraction on both the group and algebra levels.
We define twisted equivariant K-homology groups using geometric cycles. We compare them with approaches using Kasparov KK-Theory and (twisted) group C*-algebras.
We present a comprehensive theoretical framework that unifies chaotic wavefront dynamics with classical aberration theory through a Statistical Wavefront Reconstruction Framework (SWRF) formalism. By establishing rigorous connections…
The Kauffman bracket skein algebra is a quantization of the algebra of regular functions on the $SL_2$ character variety of a topological surface. We realize the skein algebra of the $4$-punctured sphere as the output of a mirror symmetry…
We derive the explicit form of the polar decomposition of the Wiener measure, and obtain the equation connecting functional integrals in conformal quantum mechanics to those in the Schwarzian theory. Using this connection we evaluate some…
We extend a result on renormalized oscillation theory, originally derived for Sturm-Liouville and Dirac-type operators on arbitrary intervals in the context of scalar coefficients, to the case of general Hamiltonian systems with block…
We study a problem of systematical evaluation of the quantum corrections for general 4D supersymmetric K\"ahler sigma models with chiral and antichiral superpotentials. Using manifestly reparametrization covariant techniques (the…
For a nonconstant holomorphic map between projective Riemann surfaces with conformal metrics, we consider invariant Schwarzian derivatives and projective Schwarzian derivatives of general virtual order. We show that these two quantities are…
Let $S$ be a smooth del Pezzo surface over a field $k$ of characteristic $\neq 2, 3$. We define an invariant in the Grothendieck-Witt ring $GW(k)$ for "counting" rational curves in a curve class $D$ of fixed positive degree (with respect to…
Recently, shearlet groups have received much attention in connection with shearlet transforms applied for orientation sensitive image analysis and restoration. The square integrable representations of the shearlet groups provide not only…
We compute the stable homology of the braid group with coefficients in any Schur functor applied to the integral reduced Burau representation. This may be considered as a hyperelliptic analogue of the Mumford conjecture (Madsen--Weiss…
Denote by $Sp(k,l)$ the quaternionic symplectic group of signature $(k,l)$. We study the deformation rigidity of the embedding $Sp(k,l) \times Sp(1) \hookrightarrow H$, where $H$ is either $Sp(k+1,l)$ or $Sp(k,l+1)$, this is done by…
We present a unified group-theoretical derivation of the Continuous Wavelet Transform (CWT) on the circle $\mathbb S^1$ and the real line $\mathbb{R}$, following the general formalism of Coherent States (CS) associated to unitary square…