Related papers: A note on the spectral flow operator

Spectral flow was first studied by Atiyah and Lusztig, and first appeared in print in the work of Atiyah-Patodi-Singer (APS). For a norm-continuous path of self-adjoint Fredholm operators in the multiplier algebra $\mathcal{M}(\mathcal{B})$…

String on $AdS_3\times S^3\times T^4$ backgrounds are known to be classically integrable in the presence of a mixture of Ramond-Ramond and Neveu-Schwarz-Neveu-Schwarz fluxes. It is expected that this results in the existence of a…

The inverse problem of spectral analysis for the non-self-adjoint matrix Sturm-Liouville operator on a finite interval is investigated. We study properties of the spectral characteristics for the considered operator, and provide necessary…

We consider bosonic string theory on $\text{AdS}_3$ supported by Kalb-Ramond flux. It is well known that the $\alpha'$ exact worldsheet theory is described by the $\text{SL(2,R)}$ WZW model. In this note we perform checks of an $\alpha'$…

We carefully examine the Polyakov path integral for strings on $\text{AdS}_3$ in superspace, both for type II and heterotic superstrings. We construct a free-field realization of the supersymmetric $\text{SL}(2,\mathbb{R})$ WZW model which…

We introduce a new topology, weaker than the gap topology, on the space of selfadjoint operators affiliated to a semifinite von Neumann algebra. We define the real-valued spectral flow for a continuous path of selfadjoint Breuer-Fredholm…

String theory on $AdS_3 \times S^3 \times T^4$ has 20 moduli. We investigate how the perturbative closed string spectrum changes as we move around this moduli space in both the RR and NSNS flux backgrounds. We find that, at weak string…

In this article we consider operators of the form $\partial_s\xi+A(s)\xi$ where $s$ lies in an interval $[-T,T]$ and $s\mapsto A(s)$ is continuous. Without boundary conditions these operators are not Fredholm. However, using interpolation…

The matrix Sturm-Liouville operator with an integrable potential on the half-line is considered. We study the inverse spectral problem, which consists in recovering of this operator by the Weyl matrix. The main result of the paper is the…

We examine the spectrum of a family of Sturm--Liouville operators with regularly spaced delta function potentials parametrized by increasing strength. The limiting behavior of the eigenvalues under this spectral flow was described in a…

In this paper we examine the asymptotic structure of the pseudospectrum of the singular Sturm-Liouville operator $L=\partial_x(f\partial_x)+\partial_x$ subject to periodic boundary conditions on a symmetric interval, where the coefficient…

In this work, we calculate correlators of long strings on AdS$_3\times$S$^3\times$T$^4$ with pure NS-NS flux. We first construct physical vertex operators that correspond to long strings. Due to the GSO projection, they depend on the parity…

String theory on AdS$_3$ with NS-NS fluxes admits a solvable irrelevant deformation which is close to the $T\bar{T}$ deformation of the dual CFT$_2$. This consists of deforming the worldsheet action, namely the action of the…

We give a comprehensive account of an analytic approach to spectral flow along paths of self-adjoint Breuer-Fredholm operators in a type $I_{\infty}$ or $II_\infty$ von Neumann algebra ${\mathcal N}$. The framework is that of {\it odd…

We develop a formalism to evaluate generic scalar exchange diagrams in AdS_{d+1} relevant for the calculation of four-point functions in AdS/CFT correspondence. The result may be written as an infinite power series of functions of…

Alday, Gaiotto, and Tachikawa conjectured relations between certain 4d N=2 supersymmetric field theories and 2d Liouville conformal field theory. We study generalizations of these relations to 4d theories with surface operators. For one…

We apply both the theory of boundary triples and perturbation theory to the setting of semi-bounded Sturm-Liouville operators with two limit-circle endpoints. For general boundary conditions we obtain refined and new results about their…

String theory on NS-NS AdS_3 x S^3 admits an exactly marginal deformation which breaks the SL(2,R)_R x SL(2,R)_L isometry of AdS_3 down to SL(2,R)_R x U(1)_L. The holographic dual is an exotic and only partially understood type of…

Let $L$ be a linear, closed, densely defined in a Hilbert space operator, not necessarily selfadjoint. Consider the corresponding wave equations &(1) \quad \ddot{w}+ Lw=0, \quad w(0)=0,\quad \dot{w}(0)=f, \quad \dot{w}=\frac{dw}{dt}, \quad…

We study Sturm-Liouville operators on closed sets of a special structure, which are sometimes referred as time scales and often appear in modelling various real processes. Depending on the set structure, such operators unify both…