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The adiabatic self-consistent collective coordinate (ASCC) method is a practical microscopic theory of large-amplitude collective motions in nuclei with superfluidity. We show that its basic equations are invariant against transformations…
By extending the method developed by Arav, Gauntlett, Roberts and Rosen, we construct supersymmetric $AdS_2\times{\Sigma}$ solutions of gauged $\mathcal{N}=8$ supergravity which are asymptotic to the $SU(3)\times{U}(1)$-invariant Warner…
We propose a new approach to solve conformal field theories and apply it to Chern-Simons Matter theories and three-dimensional bosonization duality. All three-point correlation functions of single-trace operators are obtained in the…
Using the exact solutions to the field equation for a massive scalar field on noncommutative $AdS_2$, we apply the $AdS/CFT$ correspondence principle to obtain an exact result for the associated two-point function on the conformal boundary.…
We prove that the AdS/CFT calculation of 1-point functions can be drastically simplified by using variational arguments. We give a simple universal proof, valid for any theory that can be derived from a Lagrangian, that the large radius…
We solve the Dirichlet boundary value problem for the massless gravitino on $AdS_{d+1}$ space and compute the two-point function of the dual CFT supersymmetry currents using the $AdS$/CFT correspondence principle. We find analogously to the…
Given two otherwise decoupled $D$-dimensional CFTs which possess a common (finite) symmetry subcategory, one can consider entangled boundary states of their $(D+1)$-dimensional SymTFTs. This roughly corresponds to performing a gauging of…
We construct a new class of differential operators that naturally act on AdS harmonic functions. These are weight shifting operators that change the spin and dimension of AdS representations. Together with CFT weight shifting operators, the…
It is shown that two$(1 + 1)$-dimensional (2D) free Abelian- and self-interacting non-Abelian gauge theories (without any interaction with matter fields) belong to a new class of topological field theories. These new theories capture…
Using the AdS/CFT correspondence we study vacua of N=4 SYM for which part of the gauge symmetry is broken by expectation values of scalar fields. A specific subclass of such vacua can be analyzed with gauged supergravity and the…
Boundaries in gauge field theories are known to be the locus of a wealth of interesting phenomena, as illustrated for example by the holographic principle or by the AdS/CFT and bulk-boundary correspondences. In particular, it has been…
We attempt to generalize the AdS/CFT correspondence to non-relativistic conformal field theories which are invariant under Galilean transformations. Such systems govern ultracold atoms at unitarity, nucleon scattering in some channels, and…
We consider the $\mathcal{N}=(2,2)$ AdS$_3$/CFT$_2$ dualities proposed by Eberhardt, where the bulk geometry is AdS$_3\times(S^3\times T^4)/\mathbb{Z}_k$, and the CFT is a deformation of the symmetric orbifold of the supersymmetric sigma…
In this thesis we study maximally supersymmetric solutions of gauged supergravity theories, with special focus on anti-de Sitter solutions. The latter are relevant in the context of the AdS/CFT correspondence. In the first part we classify…
In this work we discuss the cubic interactions for massless spin 3/2 gravitino with massive higher spin supermultiplets using three superblocks (2,3/2), (5/2,2) and (3,5/2) as the first non-trivial examples. We use gauge invariant formalism…
We present a general method for the analysis of the stability of static, spherically symmetric solutions to spherically symmetric perturbations in an arbitrary diffeomorphism covariant Lagrangian field theory. Our method involves fixing the…
In this dissertation, we present work towards characterizing various conformal and nearly conformal quantum field theories nonperturbatively using a combination of numerical and analytical techniques. A key area of interest is the conformal…
We study the interaction of gauge fields of arbitrary half-integer spins with the homogeneous electromagnetic field. We reduce the problem of obtaining the gauge-invariant Lagrangian and transformations of the half-integer spin fields in…
The unique off-shell fermionic gauge invariance of a vector-spinor field theory is found, and the invariant action is derived. The latter is Weyl invariant in any dimension in the massless limit, and it coincides with the singular point of…
Global symmetries play an important role in classifying the spectrum of a gauge theory. In the context of the AdS/CFT duality, global baryon-like symmetries are specially interesting. In the gravity side, they correspond to vector fields in…