We study various rotating and oscillating D-string configurations in some general backgrounds with fluxes. In particular, we look for solutions to the equations of motion of various rigidly rotating D-strings in $AdS_3$ background with mixed flux, and in the intersecting D-brane geometries. We find out relations among various conserved charges corresponding to the breathing and rotating D-string configurations.
We consider a theory of an open string moving in a weakly curved background, composed of a constant metric and a linearly coordinate dependent Kalb-Ramond field with an infinitesimal field strength. We find its T-dual using the generalized Buscher procedure developed for the closed string moving in a weakly curved background, and the fact that solving the boundary conditions, the open string theory transforms to the effective closed string theory. So, T-dualizing the effective theory along all effective directions we obtain its T-dual theory and resume the open sting theory which has such an e…
We present vertex operators for ambitwistor strings around generic Yang-Mills, gravity and NS-NS backgrounds. The requirement that vertex operators lie in the BRST cohomology of the worldsheet theory enforces the appropriate linear equations of motion (as well as gauge fixing conditions) for the respective perturbations in these backgrounds. Due to the nature of ambitwistor strings, no approximation is taken and all calculations around the backgrounds are exact.
The general fluctuations, in the form of vertex operators, for the type II superstring in the pure spinor formalism are considered. We review the construction of these vertex operators in flat space-time. We then review the type II superstrings in curved background in the pure spinor formalism to finally construct the vertex operators on a generic type II supergravity background.
The general fluctuations, in the form of vertex operators, for the heterotic superstring in the pure spinor formalism are considered. The case of a flat background is reviewed and the case of a curved case is studied. The left-moving ghosts are pure spinors and the right-moving ghosts come from fixing the reparametrization invariance. The role of the reparametrization ghosts in the construction of the vertex operators is emphasized.
The pure spinor superstring in a type II curved background is considered. In order to define reparametrization ghosts, non-minimal pure spinor variables have to be present in the formalism. The BRST transformations of the non-minimal variables are obtained. It is found that the BRST transformations of a set of world-sheet variables have the form of the corresponding transformations in flat spacetime, up to a field-dependent Lorentz rotation. This simplify the construction of the reparametrization $b$ ghosts.
The recently established B-RNS-GSS formalism is extended for the description of the heterotic superstring in curved backgrounds. We propose a generalized action and BRST charge defined in the small Hilbert space with the standard form of an $\mathcal{N}=(1,0)$ worldsheet superconformal theory with superconformal generator $G$ and stress tensor $T$. We show that $\big\{G,G\big\}=-2T$ implies the D=10 N=1 supergravity and super-Yang-Mills equations of motion, as well as holomorphicity of the BRST charge.
The string sigma model in $AdS_3\times S^3$ supported by mixed three-form fluxes has recently been proved to be integrable which led to a plethora of work in this background including proposals for S matrix and study of semiclassical string profiles. Motivated by this, in this paper, we present a study of `spiky' strings in this background. We analyze the string profiles in detail and also find the dispersion relation between the charges in the `long' string limit after solving the equations of motion perturbatively upto the leading order in the Neveu-Schwarz flux $b$. We find that the dispers…
The $AdS_3\times S^3$ string sigma model supported both by NS-NS and R-R fluxes has become a well known integrable model, however a putative dual field theory description remains incomplete. We study the anomalous dimensions of twist operators in this theory via semiclassical string methods. We describe the construction of a multi-cusp closed string in conformal gauge moving in $AdS_3$ with fluxes, which supposedly is dual to a general higher twist operator. After analyzing the string profiles and conserved charges for the string, we find the exact dispersion relation between the charges in th…
We discuss finite-size corrections to the spiky strings in $AdS$ space which is dual to the long $\mathcal{N}=4$ SYM operators of the form Tr($Δ_+ ^{J_1}ϕ_1Δ_+ ^{J_2}ϕ_2...Δ_+ ^{J_n}ϕ_n$). We express the finite-size dispersion relation in terms of Lambert $\mathbf{W}$-function. We further establish the finite-size scaling relation between energy and angular momentum of the spiky string in presence of mixed fluxes in terms of $\mathbf{W}$-function. We comment on the solution in pure NS-NS background as well.
The Yang-Mills String as the A-Model on the Twistor Space of the Complex Two-Dimensional Projective Space with Fluxes and Wilson Loops: the Beta Function
This thesis concerns the study of high-temperature string theory on curved backgrounds, generalizing the notions of Hagedorn temperature and thermal scalar to general backgrounds. Chapter 2 contains a review on string thermodynamics in flat space, setting the stage. Chapters 3 and 4 contain the detailed study of the random walk picture in a general curved background. Chapters 5 and 6 then apply this to Rindler space, the near-horizon approximation of a generic (uncharged) black hole. Chapters 7 and 8 contain a study of the AdS3 and BTZ WZW models where we study the thermal spectrum and the res…
