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We study high-harmonic generation in two-dimensional electron systems with Rashba and Dresselhaus spin-orbit coupling and derive harmonic generation selection rules with the help of group theory. Based on the bandstructures of these minimal…
We propose a universal geometric formulation of gauged supergravity in terms of a twisted doubled torus. We focus on string theory (M-theory) reductions with generalized Scherk-Schwarz twists residing in the O(n,n) (E_{7(7)}) duality group.…
Given a gerbe $L$, on the holonomy groupoid $\mathcal G$ of the foliation $(M, \mathcal F)$, whose pull-back to $M$ is torsion, we construct a Connes $\Phi$-map from the twisted Dupont-Sullivan bicomplex of $\mathcal G$ to the cyclic…
We introduce a new, algebraic method to construct duality functions for integrable dynamic models. This method will be implemented on dynamic stochastic higher spin vertex models, where we prove the duality functions are the $ _3 \varphi_2$…
The author makes use of infinite compositions and a limiting function to construct a $\mathcal{C}^\infty$ tetration function $\mathcal{F}(t) = e \tet t$. As a tetration function, $\mathcal{F}$ satisfies $e^{\mathcal{F}(t)} =…
We generalize Regge theory to correlation functions in conformal field theories. This is done by exploring the analogy between Mellin amplitudes in AdS/CFT and S-matrix elements. In the process, we develop the conformal partial wave…
In this work, we study a class of higher derivative couplings in the string effective action arising at the junction of topological string theory and supersymmetric gauge theories in the $\Omega$-background. They generalise a series of…
We employ the intertwining operator technique to synthesize a supersymmetric (SUSY) array of arbitrary size $N$. The synthesized SUSY system is equivalent to a spin-$(N-1)/2$ under an effective magnetic field. By considering an additional…
Extensions of standard one-dimensional supersymmetric quantum mechanics are discussed. Supercharges involving higher order derivatives are introduced leading to an algebra which incorporates a higher order polynomial in the Hamiltonian. We…
Spectral flow in two-dimensional field theories is known to correspond to geometrical twisting between two circles in the gravity dual. We generalize this operation to the geometries which have SO(k+1) x SO(k+1) isometries with k>1 and…
A semiclassical approach is proposed to calculate the collective potential and mass parameters to formulate a collective Hamiltonian capable of describing the wobbling motion in both even-even and odd-mass systems. By diagonalizing the…
Weihrauch reducibility is a notion of reducibility between computational problems that is useful to calibrate the uniform computational strength of a multivalued function. It complements the analysis of mathematical theorems done in reverse…
We review new aspects of integrable systems discovered recently in N=2 supersymmetric gauge theories and their topologically twisted versions. The main topics are (i) an explicit construction of Whitham deformations of the Seiberg-Witten…
We generalize a construction of Dunkl, obtaining a wide class intertwining functions on the symmetric group and a related family of multidimensional Hahn polynomials. Following a suggestion of Vilenkin and Klymik, we develop a tree-method…
We give a uniform, Lie-theoretic mirror symmetry construction for the Frobenius manifolds defined by Dubrovin-Zhang in arXiv:hep-th/9611200 on the orbit spaces of extended affine Weyl groups, including exceptional Dynkin types. The B-model…
We derive strong estimates for Schatten norms of operator derivatives along paths of contractions and apply them to prove existence of higher order spectral shift functions for pairs of contractions.
We study anomalous dimensions of unprotected low twist operators in the four-dimensional $SU(N)$ $\mathcal{N}=4$ supersymmetric Yang-Mills theory. We construct a class of interpolating functions to approximate the dimensions of the leading…
The accurate computation of low-energy spectra of strongly correlated quantum many-body systems, typically accessed via Green's-functions, is a long-standing problem posing enormous challenges to numerical methods. When the spectral…
We give a complete classification of twists of supersymmetric Yang--Mills theories in dimensions $2\leq n \leq 10$. We formulate supersymmetric Yang--Mills theory classically using the BV formalism, and then we construct an action of the…
Some basic facts about the prepotential in the SW/Whitham theory are presented. Consideration begins from the abstract theory of quasiclassical $\tau$-functions , which uses as input a family of complex spectral curves with a meromorphic…