We provide a field theory interpretation of the attractor mechanism for asymptotically AdS$_4$ dyonic BPS black holes whose entropy is captured by the supersymmetric index of the twisted ABJM theory at Chern-Simons level one. We holographically compu
te the renormalized off-shell quantum effective action in the twisted ABJM theory as a function of the supersymmetric fermion masses and the arbitrary vacuum expectation values of the dimension one scalar bilinear operators and show that extremizing the effective action with respect to the vacuum expectation values of the dimension one scalar bilinears is equivalent to the attractor mechanism in the bulk. In fact, we show that the holographic quantum effective action coincides with the entropy functional and, therefore, its value at the extremum reproduces the black hole entropy.
We present a large class of new backgrounds that are solutions of type II supergravity with a warped AdS${}_4$ factor, non-trivial axion-dilaton, B-field, and three- and five-form Ramond-Ramond fluxes. We obtain these solutions by applying non-Abelia
n T-dualities with respect to SU(2) or SU(2)/U(1) isometries to reductions to 10d IIA of 11d sugra solutions of the form AdS${}_4 times Y^7$, with $Y^7 = S^7/mathbb{Z}_k, S^7, M^{1,1,1}, Q^{1,1,1}$ and $N(1,1)$. The main class of reductions to IIA is along the Hopf fiber and leads to solutions of the form $AdS_4 times K_6$, where $K_6 $ is Kahler Einstein with $K_6=mathbb{CP}^3, S^2times mathbb{CP}^2, S^2times S^2 times S^2$; the first member of this class is dual to the ABJM field theory in the t Hooft limit. We also consider other less symmetric but susy preserving reductions along circles that are not the Hopf fiber. In the case of $N(1,1)$ we find an additional breaking of isometries in the NAT-dual background. To initiate the study of some properties of the field theory dual, we explicitly compute the central charge holographically.
We present a large class of new backgrounds that are solutions of type IIB supergravity with a warped AdS${}_5$ factor, non-trivial axion-dilaton, $B$-field and three-form Ramond-Ramond flux but yet have no five-form flux. We obtain these solutions a
nd many of their variations by judiciously applying non-Abelian and Abelian T-dualities, as well as coordinate shifts to AdS${}_5times X_5$ IIB supergravity solutions with $X_5=S^5, T^{1,1}, Y^{p,q}$. We address a number of issues pertaining to charge quantization in the context of non-Abelian T-duality. We comment on some properties of the expected dual super conformal field theories by studying their CFT central charge holographically. We also use the structure of the supergravity Page charges, central charges and some probe branes to infer aspects of the dual super conformal field theories.
The leading term for the energy of a bound state of k-quarks and k-antiquarks is proportional to its separation L. These k-string configurations have a Luscher term associated with their quantum fluctuations which is typically a 1/L correction to the
energy. We review the status of tensions and Luscher terms in the context of lattice gauge theory, Hamiltonian methods, and gauge/gravity correspondence. Furthermore we explore how different representations of the k-string manifest themselves in the gauge/gravity duality. We calculate the Luscher term for a strongly coupled SU(N) gauge theory in (2+1) dimensions using the gauge/gravity correspondence. Namely, we compute one-loop corrections to a probe D4-brane embedded in the Cvetic, Gibbons, Lu, and Pope supergravity background. We investigate quantum fluctuations of both the bosonic and the fermionic sectors.
We perform a systematic analysis of k-strings in the framework of the gauge/gravity correspondence. We discuss the Klebanov-Strassler supergravity background which is known to be dual to a confining supersymmetric gauge theory with chiral symmetry br
eaking. We obtain the k-string tension in agreement with expectations of field theory. Our main new result is the study of one-loop corrections on the string theoretic side. We explicitly find the frequency spectrum for both the bosons and the fermions for quadratic fluctuations about the classical supergravity solution. Further we use the massless modes to compute 1/L contributions to the one loop corrections to the k-string energy. This corresponds to the Luscher term contribution to the k-string potential on the gauge theoretic side of the correspondence.
An important operation in generalized complex geometry is the Courant bracket which extends the Lie bracket that acts only on vectors to a pair given by a vector and a p-form. We explore the possibility of promoting the elements of the Courant bracke
t to physical fields by constructing a geometric action based on the Kirillov-Kostant symplectic form. For the $p=0$ forms, the action generalizes Polyakovs two-dimensional quantum gravity when viewed as the geometric action for the Virasoro algebra. We show that the geometric action arising from the centrally extended Courant bracket for the vector and zero form pair is similar to the geometric action obtained from the semi-direct product of the Virasoro algebra with a U(1) affine Kac-Moody algebra. For arbitrary $p$ restricted to a Dirac structure, we derived the geometric action and exhibit generalizations for almost complex structures built on the Kirillov-Kostant symplectic form. In the case of p+1 dimensional submanifolds, we also discuss a generalization of a Kahler structure on the orbits.
