Related papers: Modular Constraints on Superconformal Field Theori…
We classify the large $N$ limits of four-dimensional supersymmetric gauge theories with simple gauge groups that flow to superconformal fixed points. We restrict ourselves to the ones without a superpotential and with a fixed flavor…
In this paper we begin mapping out the space of rank-2 $\mathcal{N}=2$ superconformal field theories (SCFTs) in four dimensions. This represents an ideal set of theories which can be potentially classified using purely quantum…
We study weakly coupled $U(1)$ theories in $AdS_3$, their associated charged BTZ solutions, and their charged spectra. We find that modular invariance of the holographic dual two-dimensional CFT and compactness of the gauge group together…
In this thesis, the AdS/CFT correspondence is used as a tool to explore novel AdS$_5$ Supergravity backgrounds (containing five-dimensional Anti-de Sitter spacetime) and their dual (four dimensional) Conformal Field Theory descriptions. In…
We use modular invariance and crossing symmetry of conformal field theory to reveal approximate reflection symmetries in the spectral decompositions of the partition function in two dimensions in the limit of large central charge and of the…
We study the instanton partition functions of two well-known superconformal field theories with mass deformations. Two types of anomaly equations, namely, the modular anomaly and holomorphic anomaly, have been discovered in the literature.…
In this paper we investigate three-dimensional superconformal gauge theories with N=3 supersymmetry. Independently from specific models, we derive the shortening conditions for unitary representations of the Osp(3|4) superalgebra and we…
We give an elementary proof of the following property of unitary, interacting four-dimensional $\mathcal{N}=2$ superconformal field theories: at large central charge $c$, there exist at least $\sqrt{c}$ single-trace, scalar superconformal…
We introduce the analytic superspace formalism for six-dimensional $(N,0)$ superconformal field theories. Concentrating on the $(2,0)$ theory we write down the Ward identities for correlation functions in the theory and show how to solve…
We use holography and four-dimensional $\,\mathcal{N}=4\,$ gauged supergravity to collect evidence for a large class of interconnected three-dimensional $\,\mathcal{N}=2\,$ conformal field theories. On the gravity side, we construct a…
We study superconformal deformations of the $T_\rho^{\hat\rho}[SU(N)]$ theories of Gaiotto-Hanany-Witten, paying special attention to mixed-branch operators with both electrically- and magnetically-charged fields. We explain why all…
We prove versions of super spin-charge separation for all three of the symmetry groups SU(N), Sp(2N), and SO(N) of disordered Dirac fermions in 2+1 dimensions, which involve the supercurrent-algebras gl (1|1)_{N}, osp(2|2)_{-2N}, and…
We study the large N operator spectrum of the (1,0) superconformal chiral six-dimensional theory with E_8 global symmetry. This spectrum is dual to the Kaluza-Klein spectrum of supergravity on AdS_7 X S^4/Z_2 with a ten-dimensional E_8…
Global conformal invariance determines the form of two and three-point functions of quasi-primary operators in a conformal field theory, and generates nontrivial relations between terms in the operator product expansion. These ideas are…
Various observables in compact CFTs are required to obey positivity, discreteness, and integrality. Positivity forms the crux of the conformal bootstrap, but understanding of the abstract implications of discreteness and integrality for the…
In this paper we introduce the characteristic dimension of a four dimensional $\mathcal{N}=2$ superconformal field theory, which is an extraordinary simple invariant determined by the scaling dimensions of its Coulomb branch operators. We…
We study the spectrum of scalar primary operators in any two-dimensional conformal field theory. We show that the scalars alone obey a nontrivial crossing equation. This extends previous work that derived a similar equation for Narain…
Motivated by the observation that $2+2=4$, we consider four-dimensional $\mathcal{N}=2$ superconformal field theories on $S^2\times\Sigma$, turning on a suitable rigid supergravity background. On the one hand, reduction of a…
We study the one-loop partition function of superstrings in the $\mathrm{AdS}_3 \times \mathbf{S}^3 \times \mathbf{S}^3 \times \mathbf{S}^1$ background. Specifically, we show that the supergravity spectrum, which contains non-chiral primary…
We describe the constraints imposed on quantum maximal supergravity theories in perturbation theory by the two duality frameworks: S-duality in superstring theory and the AdS/CFT holographic correspondence between IIB superstring theory and…