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We have studied a model which has been proposed as a regularisation for four dimensional quantum gravity. The partition function is constructed by performing a weighted sum over all triangulations of the four sphere. Using numerical…

We construct a new $N=4$ non-semisimple gauged supergravity in three dimensions with $E_{6(2)}/SU(6)\times SU(2)$ scalar manifold and $SO(4)\ltimes \mathbf{T}^6$ gauge group. Depending on the values of the gauge coupling constants, the…

A prescription is given for computing anomalous dimensions of single trace operators in SYM at strong coupling and large $N$ using a reduced model of matrix quantum mechanics. The method involves treating some parts of the operators as "BPS…

Gaiotto and Witten found that one can construct 3d $\mathcal{N}=4$ Chern-Simons matter theories by using $\mathcal{N}=4$ SCFT whose momentum map of global symmetries satisfy special condition. Usually, one uses free hypermultiplet and…

This PhD thesis is devoted to the study of supersymmetry preserving background solutions of N=2 supergravity in 4 dimensions. The main contents are divided into three major parts, briefly summarized as follows. Part I deals with analysis of…

We investigate the exact results for circular 1/4 and 1/2 BPS Wilson loops in the $d=3$ ${\mathcal N}=4$ super Chern-Simons-matter theory that could be obtained by orbifolding Aharony-Bergman-Jafferis-Maldacena (ABJM) theory. The partition…

We fix the long-standing ambiguity in the 1-loop contribution to the mass of a 1+1-dimensional supersymmetric soliton by adopting a set of boundary conditions which follow from the symmetries of the action and which depend only on the…

We provide some upper bounds for the Mertens function ($M(n)$: the cumulative sum of the M$\ddot{\mathrm{o}}$bius function) by an approach of statistical mechanics, in which the M$\ddot{\mathrm{o}}$bius function is taken as a particular…

We study the commutative limit of the non-commutative maximally supersymmetric Yang-Mills theory in four dimensions (N=4 SYM). The commutative limits of non-commutative spaces are important in particular in the applications of…

We examine the partition function of N=2* supersymmetric SU(N) Yang-Mills theory on the four-sphere in the large radius limit. We point out that the large radius partition function, at fixed N, is computed by saddle points lying on…

The stability of the kinks of the non-linear ${\mathbb S}^2$-sigma model discovered in Phys. Rev. Lett. 101(2008)131602 is discussed from several points of view. After a direct estimation of the spectra of the second-order fluctuation…

We study exact correlation functions of N=4 SYM at zero coupling. It has been known that it is convenient to label local gauge invariant operators by irreducible representations of symmetric groups/Brauer algebras. We first review the…

We claim that if by a choice of the couplings the theory can be made conformally invariant (vanishing of the beta functions) it is automatically finite and vice versa. This is demonstrated by explicit example in supersymmetric gauge theory.…

We derive the first $\epsilon_2$-correction to the instanton partition functions of $\mathcal{N}=2$ Super Yang-Mills (SYM) in four dimensions in the Nekrasov-Shatashvili limit $\epsilon_2\rightarrow 0$. In the latter we recall the emergence…

We study the expansion near roots of unity of the superconformal index of 4d $SU(N)$ $\mathcal{N}=4$ SYM. In such an expansion, middle-dimensional walls of non-analyticity are shown to emerge in the complex analytic extension of the…

We present a new massive theory of superspin Y=3/2 which has non-minimal supergravity as it's massless limit. The new result will illuminate the underlying structure of auxiliary fields required for the description of arbitrary massive…

We consider three-dimensional ${\mathcal N}=2$ supersymmetric field theories defined on general complex-valued backgrounds of Euclidean new minimal supergravity admitting two Killing spinors of opposite $R$-charges. We compute partition…

String theory on AdS$_3$ $\times$ S$^3$ $\times$ $\mathcal{M}_4$ provides a well-studied realization of AdS$_3$/CFT$_2$ holography, but its non-perturbative structure at finite $N \sim 1/G_N^{(3)}$ is largely unknown. A long-standing puzzle…

We consider supersymmetric gauge theories on $S^5$ with a negative Yang-Mills coupling in their large $N$ limits. Using localization we compute the partition functions and show that the pure ${\mathrm{SU}}(N)$ gauge theory descends to an…

In this report we compute the boundary states (including the boundary entropy) for the boundary sine-Gordon theory. From the boundary states, we derive both correlation and partition functions. Through the partition function, we show that…