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Only a severely restricted class of tensor fields can provide classical spacetime geometries, namely those that can carry matter field equations that are predictive, interpretable and quantizable. These three conditions on matter translate…
We derive the necessary and sufficient conditions under which the general Plebanski-Demianski (PD) solution of Einstein-Maxwell theory with a negative cosmological constant admits Killing spinors. We consider in detail two different scaling…
We consider higher dimensional gravity in which the four dimensional spacetime and extra dimensions are not treated on an equal footing. The anisotropy is implemented in the ADM decomposition of higher dimensional metric by requiring the…
It is pointed out that various types of cosmic string solutions that exist in nonsupersymmetric and globally supersymmetric theories, such as D-type gauge strings, F-type global and gauge strings, and superconducting Witten strings, also…
When four scalar fields with global Lorentz symmetry are coupled to gravity and take a vacuum expectation value breaking diffeomorphism invariance spontaneously, the graviton becomes massive. This model is supersymmetrized by considering…
The Randall-Sundrum model is studied in 6 dimension with AdS$_4$ or dS$_4$ metric in the physical 4 dimensional space. Two solutions are found, one with induced 5-dimensional gravity terms added to the induced cosmological constant terms.…
For the solid-on-solid (SOS) model with spin values from the set of all integers on a Cayley tree we give gradient Gibbs measures (GGMs). Such a measure corresponds to a boundary law (which is an infinite-dimensional vector-valued function…
We examine the black hole solutions of dS$_3$ gravity by applying the explicit dS$_3$/CFT$_2$ correspondence. The gravity theory is described by Chern-Simons theory with complex gauge group SL$(2,\mathbb{C})$, and the complexified theory is…
Continuous symmetries of spacetime such as spatial homogeneity and isotropy are rigorously defined using the concept of isometries and Killing vectors. In supergravity, the metric, or rather the tetrad, is not a standalone entity, but is…
This note gives a brief review of the integrable structures presented in the Seiberg-Witten approach to the N=2 SUSY gauge theories with emphasize on the case of the gauge theories with matter hypermultiplets included (described by spin…
Using the tractor calculus to study smooth metric measure spaces, we adapt results of Gover and Nurowski to give sharp metric obstructions to the existence of quasi-Einstein metrics on suitably generic manifolds. We do this by introducing…
Six-dimensional chiral gauged Einstein-Maxwell supergravity admits a two-parameter rotating dyonic string solution whose near horizon limit is the direct product of AdS$_3$ and a squashed three-sphere $S^3$. For a particular relation…
We reconsider the problem of bounding higher derivative couplings in consistent weakly coupled gravitational theories, starting from general assumptions about analyticity and Regge growth of the S-matrix. Higher derivative couplings are…
We determine complex saddles of three-dimensional gravity with a positive cosmological constant by applying the recently proposed holography. It is sometimes useful to consider a complexified metric to study quantum gravity as in the case…
We present a field theory description for the non-perturbative splitting and joining of baby universes in Euclidean Jackiw-Teitelboim (JT) gravity. We show how the gravitational path integral, defined as a sum over topologies, can be…
The Kaluza-Klein spectrum of N=2, D=4 supergravity compactified on AdS_2 x S^2 is found and shown to consist of two infinite towers of SU(1,1|2) representations. In addition to `pure gauge' modes living on the boundary of AdS which are…
This thesis is devoted to the study of three problems on the Wess-Zumino-Witten (WZW) and Chern-Simons (CS) supergravity theories in the Hamiltonian framework: 1) The two-dimensional super WZW model coupled to supergravity is constructed.…
We propose a hybrid class of theories for higher spin gravity and matrix models, i.e. which handle simultaneously higher spin gravity fields and matrix models. The construction is similar to Vasiliev's higher spin gravity but part of the…
Witten's Gauged Linear $\sigma$-Model (GLSM) unifies the Gromov-Witten theory and the Landau-Ginzburg theory, and provides a global perspective on mirror symmetry. In this article, we summarize a mathematically rigorous construction of the…
Second-order superintegrable systems in dimensions two and three are essentially classified. With increasing dimension, however, the non-linear partial differential equations employed in current methods become unmanageable. Here we propose…