Quasi-normal Modes of AdS5 Black Hole at $\mathcal{N}=2$ Supergravity

In this paper we consider the AdS ₅ black hole at the \(\mathcal{N}=2\) supergravity background. By using the AdS/CFT correspondence we discuss about the quasi-normal modes of the scalar field in the black hole, which is dual of the scalar glueballs spectrum on the boundary. We obtain phase transition conditions from stable to unstable theory, which interpreted as confinement and deconfinement states in the QCD. We obtain the specific heat in terms of the temperature and charge of black hole, we find the temperature where the black hole is stable. Also we rewrite the equation of motion in the Schrödinger form and discuss the effective potential.     

Chiral dynamics and meson with non-commutative dipole field in gauge/gravity dual

Apply the T-duality and smeared twist to the D3-brane solution one can construct the supergravity backgrounds which may dual to supersymmetric or non-supersymmetric non-commutative dipole field theory. We introduce D7-brane probe into the dual supergravity background to study the chiral dynamics and meson spectrum therein. We first find that the non-commutative dipole field does not induce the chiral symmetry breaking even if the supersymmetry was completely broken, contrast to the conventional believing that the chiral symmetry will be broken in the non-supersymmetric theory. Next, we find that the dipole field does not modify the meson spectrum in the supersymmetric theory while it will reduce the meson bound-state energy in the non-supersymmetric theory. We also evaluate the static quark–anti-quark potential and see that the dipole field has an effect to produce attractive force between the quark and anti-quark.     

{\mathcal{N} = 2} Supersymmetric AdS4 Solutions of M-theory

We analyse the most general ${\mathcal{N} = 2}$ supersymmetric solutions of D = 11 supergravity consisting of a warped product of four-dimensional anti-de-Sitter space with a seven-dimensional Riemannian manifold Y ₇. We show that the necessary and sufficient conditions for supersymmetry can be phrased in terms of a local SU(2)-structure on Y ₇. Solutions with non-zero M2-brane charge also admit a canonical contact structure, in terms of which many physical quantities can be expressed, including the free energy and the scaling dimensions of operators dual to supersymmetric wrapped M5-branes. We show that a special class of solutions is singled out by imposing an additional symmetry, for which the problem reduces to solving a second order non-linear ODE. As well as recovering a known class of solutions, that includes the IR fixed point of a mass deformation of the ABJM theory, we also find new solutions which are dual to cubic deformations. In particular, we find a new supersymmetric warped AdS₄ × S ⁷ solution with non-trivial four-form flux.     

The G2 invariant compactifications in eleven-dimensional supergravity

In this article we study the most general compactifications of eleven-dimensional supergravity to four-dimensional anti-de Sitter space, using a seven-dimensional internal compact manifold whose local isometry group contains the exceptional group, G₂. We find that the only such compactifications are the well known ones involving the round seven-sphere. We discuss the implications of this result for conjectured relationship between the eleven-dimensional theory and gauged N = 8 supergravity.     

Linear bosonic and fermionic quantum gauge theories on curved spacetimes

We develop a general setting for the quantization of linear bosonic and fermionic field theories subject to local gauge invariance and show how standard examples such as linearised Yang-Mills theory and linearised general relativity fit into this framework. Our construction always leads to a well-defined and gauge-invariant quantum field algebra, the centre and representations of this algebra, however, have to be analysed on a case-by-case basis. We discuss an example of a fermionic gauge field theory where the necessary conditions for the existence of Hilbert space representations are not met on any spacetime. On the other hand, we prove that these conditions are met for the Rarita-Schwinger gauge field in linearised pure $N=1$ supergravity on certain spacetimes, including asymptotically flat spacetimes and classes of spacetimes with compact Cauchy surfaces. We also present an explicit example of a supergravity background on which the Rarita-Schwinger gauge field can not be consistently quantized.     

Thermodynamics in rotating anti-de Sitter black holes with massive scalar field in three dimensions

We investigated the tendency in the variations of CFT₂ when a rotating AdS₃ black hole changes because of the fluxes transferred by the scattering of a massive scalar field according to the anti-de Sitter (AdS)/conformal field theory (CFT) correspondence. The conserved quantities of the black hole are definitely constrained by the extremal condition. Moreover, the laws of thermodynamics provide a direction for the changes in the conserved quantities. Therefore, the black hole cannot be extremal under the scattering; this is naturally preferred. According to the relationship between the rotating AdS₃ black hole and dual CFT₂, we find that such changes in the black hole constrain the variations in the eigenstates of dual CFT₂. Furthermore, the tendency in the variations is closely related to the laws of thermodynamics.     

Magnetovacs in gauged N = 4 supergravity

A two-parameter family of supersymmetric background field solutions of the recently formulated version of gauged N = 4 supergravity is found. This constitutes strong evidence that the theory has stable vacua, despite energy densities that are unbounded below. The background geometries are metric products of (AdS)₂ × S₂, and there are covariantly constant magnetic and electric fields. For a special choice of parameters the (AdS)₂ factor becomes a flat Minkowski space and electric fields vanish.     

Black holes in Gödel universes and pp waves

We find exact solutions for rotating and nonrotating neutral black holes in the G?del universe of five-dimensional minimal supergravity theory. We also describe the embedding of this solution in M-theory. After dimensional reduction and T-duality, we obtain a supergravity solution corresponding to placing a black string in a pp-wave background.     

Quark confinement in 2+1 dimensional pure Yang-Mills theory

We report some progress on the quark confinement problem in 2 + 1 dim. pure Yang-Mills theory, using Euclidean instanton methods. The instantons are regularized Wu-Yang ‘monopoles’, whose long range Coulomb field is screened by collective effects. Such configurations are stable to small perturbations unlike the case of singular, undressed monopoles. Using exact non-perturbative results for the 3-dim. Coulomb gas, where Debye screening holds for arbitrarily low temperatures, we show in a self-consistent way that a mass gap is dynamically generated in the gauge theory. The mass gap also determines the size of the monopoles. We also identify the disorder operator of the model in terms of the Sine-Gordon field of the Coulomb gas and hence obtain a dual representation whose symmetry is the centre ofSU(2).     

New D = 10, N = 1 superspace supergravity and local symmetries of superstrings

The superspace formulation of new D = 10, N = 1 supergravity is developed. It is shown that the background superspace of the new theory can be coupled to a test superstring in such a way that the local symmetries of the superstring are intact. This formulation necessarily makes use of the Vainberg construction so the action is analogous to the effective action for QCD with the WZW term. The results suggest that the ambiguity between the massless two-form and six-form in the SO(32) or E₈ × E₈ superstring theories can only be resolved by a gauge invariant, Lorentz-covariant formulation of superstring field theory.     

Holography at an extremal De Sitter horizon

Rotating maximal black holes in four-dimensional de Sitter space, for which the outer event horizon coincides with the cosmological horizon, have an infinite near-horizon region described by the rotating Nariai metric. We show that the asymptotic symmetry group at the spacelike future boundary of the near-horizon region contains a Virasoro algebra with a real, positive central charge. This is evidence that quantum gravity in a rotating Nariai background is dual to a two-dimensional Euclidean conformal field theory. These results are related to the Kerr/CFT correspondence for extremal black holes, but have two key differences: one of the black hole event horizons has been traded for the cosmological horizon, and the near-horizon geometry is a fiber over dS₂ rather than AdS₂.     

A chiral theory of nucleons

We present arguments that QCD at low momenta is reduced to a simple theory given by a path integral over pion fields and quarks which obtain dynamical mass owing to chiral symmetry breaking. The dimensional quantities of this low-momenta theory are fixed through the Λ_QCD parameter. The effective chiral lagrangian is given by a quark determinant in a background chiral field. Its properties are investigated both for slowly and rapidly varying pion fields. Though it satisfies requirements known from theory and phenomenology, it does not possess non-trivial soliton solutions. However we show that, at large N_c, nucleons correspond not to the local minimum of the effective chiral lagrangian but to a minimum of a more subtle quantity. In general, different functionals of the chiral field should be minimized, depending on the baryon charge of the system.We obtain a quantitative picture of nucleons as localized states of “constituent” quarks bound by a self-consistent pion field. Its properties, such as electromagnetic form factors, etc., are investigated in detail. We get very reasonable numerical values for the nucleon static properties.     

A dual formulation of supergravity-matter theories

Generating supersymmetric AdS solutions in non-minimal supergravity in four dimensions is notoriously difficult. Indeed, it is a longstanding lore that such solutions exist only for old minimal supergravity. In this paper, we construct a dual formulation for general N=1 supergravity-matter systems that avoids the problem. In the case of pure supergravity without a cosmological constant, it coincides with the usual non-minimal (n=−1) supergravity, but in the presence of matter (or a cosmological constant) our formulation differs considerably. We also elaborate upon the framework of conformal superspace and the compensator method as applied to our theory. In particular, we show that one can encode the details of the Kähler potential and superpotential entirely within the geometry of superspace so that the general sigma-model action is encoded in a single compact term: the supervolume. Finally, we discuss the issue of supercurrents and propose a general form for the supercurrent in AdS.     

Construction of local meson operator from the path-ordered operator in QCD2

A local meson operator is constructed from the path-ordered operator on QCD₂. The meson operator satisfies the Klein-Gordon equation with the mass identical to the eigenvalue of the 't Hooft equation. The interaction of the meson is shown to be nonlocal and to have a coupling proportional to 1/N_c.