Non-conformal Backgrounds Research Articles

Extending the scope of holographic mutual information and chaotic behavior

We extend the use of holography to investigate the scrambling properties of various physical systems. Specifically, we consider: (i) non-conformal backgrounds of black $Dp$ branes, (ii) asymptotically Lifshitz black holes, and (iii) black $AdS$ solutions of Gauss-Bonnet gravity. We use the disruption of the entanglement entropy as a probe of the chaotic features of such systems. Our analysis shows that these theories share the same type of behavior as conformal theories as they undergo chaos; however, in the case of Gauss-Bonnet gravity, we find a stark difference in the evolution of the mutual information for negative Gauss-Bonnet coupling. This may signal an inconsistency of the latter.

Corner contributions to holographic entanglement entropy in non-conformal backgrounds

We study corner contributions to holographic entanglement entropy in non-conformal backgrounds: a kink for D2-branes as well as a cone and two different types of crease for D4-branes. Unlike 2+1-dimensional CFTs, the corner contribution to the holographic entanglement entropy of D2-branes exhibits a power law behaviour rather than a logarithmic term. However, the logarithmic term emerges in the holographic entanglement entropy of D4-branes. We identify the logarithmic term for a cone in D4-brane background as the universal contribution under appropriate limits and compare it with other physical quantities.

Entanglement thermodynamics for nonconformal D-branes

We study thermodynamics of entanglement entropy for weakly excited states in certain non-conformal fields theories, whose gravity duals are given by non-conformal Dp-branes. We observe that the entanglement entropy of a sufficiently small system in non-conformal backgrounds still obeys a first-law like relation, just as the AdS counterparts investigated in arXiv: 1212.1164 [hep-th]. The effective temperature is proportional to the inverse of the size of the subsystem. The proportionality is a dimensionless constant which is only determined by the shape of the entangling region and independent of any coupling. This universality is confirmed by working with the ten-dimensional string frame metric as well as the lower-dimensional effective metric. When the entangling region is a strip and translational invariance is broken by metric fluctuations, we derive a first-law like relation where additional components of the stress energy tensor are involved.

Multiplicities from black-hole formation in heavy-ion collisions

Abstract The formation of trapped surfaces in the head-on collision of shock waves in conformal and non-conformal backgrounds is investigated. The backgrounds include all interesting confining and non-confining backgrounds that may be relevant for QCD. Several transverse profiles of the shocks are investigated including distributions that fall-off as powers or exponentials. Different ways of cutting-off the UV contributions (that are expected to be perturbative in QCD) are explored. Under some plausible simplifying assumptions our estimates are converted into predictions for multiplicities for heavy-ion collisions at RHIC and LHC.

Wilson loops stability in the gauge/string correspondence

We study the stability of some classical string worldsheet solutions employed for computing the potential energy between two static fundamental quarks in confining and non-confining gravity duals. We discuss the fixing of the diffeomorphism invariance of the string action, its relation with the fluctuation orientation and the interpretation of the quark mass substraction worldsheet needed for computing the potential energy in smooth (confining) gravity background. We consider various dual gravity backgrounds and show by a numerical analysis the existence of instabilities under linear fluctuations for classical string embedding solutions having positive length function derivative $L'(r_0)>0$. Finally we make a brief discussion of 't Hooft loops in non-conformal backgrounds.

Exploring colourful holographic superconductors

We explore a class of holographic superconductors built using non-abelian condensates on probe branes in conformal and non-conformal backgrounds. These are shown to exhibit behaviour of the specific heat which resembles that of heavy fermion compounds in the superconducting phase. Instead of showing BCS-like exponential behaviour, the specific heat is polynomial in the temperature. It exhibits a jump at the critical temperature, in agreement with real-world superconductors. We also analyse the behaviour of the energy gap and the AC and DC conductivities, and find that the systems can be either semi-conducting or metallic just above the critical temperature.

PP-wave holography for D p-brane backgrounds

As an extension of the so-called BMN conjecture, we investigate the plane-wave limit for possible holographic connection between bulk string theories in nonconformal backgrounds of D p-branes and the corresponding supersymmetric gauge theories for p<5. Our work is based on the tunneling picture for dominant null trajectories of strings in the limit of large angular momentum. The tunneling null trajectories start from the near-horizon boundary and return to the boundary, and the resulting backgrounds are time-dependent for general D p-branes except for p=3. We develop a general method for extracting diagonalized two-point functions for boundary theories as Euclidean (bulk) S-matrix in the time-dependent backgrounds. For the case of D0-brane, two-point functions of supergravity modes are shown to agree with the results derived previously by the perturbative analysis of supergravity. We then discuss the implications of the holography for general cases of D p-branes including the stringy excitations. All the cases ( p≠3, p<5) exhibit interesting infra-red behaviors, which are different from free-field theories, suggesting the existence of quite nontrivial fixed-points in dual gauge theories.

On Penrose limits and gauge Theories

We discuss various Penrose limits of conformal and nonconformal backgrounds. In AdS_5 x T^{1,1}, for a particular choice of the angular coordinate in T^{1,1} the resulting Penrose limit coincides with the similar limit for AdS_5 x S^5. In this case an identification of a subset of field theory operators with the string zero modes creation operators is possible. For another limit we obtain a light-cone string action that resembles a particle in a magnetic field. We also consider three different types of backgrounds that are dual to nonconformal field theories: The Schwarzschild black hole in AdS_5, D3-branes on the small resolution of the conifold and the Klebanov-Tseytlin background. We find that in all three cases the introduction of nonconformality renders a theory that is no longer exactly solvable and that the form of the deformation is universal. The corresponding world sheet theory in the light-cone gauge has a \tau=x^+ dependent mass term.

UV-IR relations in AdS dynamics

We point out that two distinct distance-energy relations have been discussed in the AdS-CFT correspondence. In conformal backgrounds they differ only in normalization, but in nonconformal backgrounds they differ in functional form. We discuss the relation to probe processes, the holographic principle, and black hole entropies.

Quantum string dynamics in the conformal invariantSL(2,R)WZWN background: Anti–de Sitter space with torsion

We consider classical and quantum strings in the conformally invariant background corresponding to the $\mathrm{SL}(2,R)$ WZWN model. This background is locally anti--de Sitter spacetime with non-vanishing torsion. Conformal invariance is expressed as the torsion being parallelizing. The precise effect of the conformal invariance on the dynamics of both circular and generic classical strings is extracted. In particular, the conformal invariance gives rise to a repulsive interaction of the string with the background which precisely cancels the dominant attractive term arising from gravity. We perform both semi-classical and canonical string quantization, in order to see the effect of the conformal invariance of the background on the string mass spectrum. Both approaches yield that the high-mass states are governed by $m\ensuremath{\sim}\mathrm{HN}$ ($N\ensuremath{\in}{N}_{0},$ $N$ ``large''), where $m$ is the string mass and $H$ is the Hubble constant. It follows that the level spacing grows proportionally to ${N:d(m}^{2}{\ensuremath{\alpha}}^{\ensuremath{'}})/dN\ensuremath{\sim}N,$ while the string entropy goes like $S\ensuremath{\sim}\sqrt{m}.$ Moreover, it follows that there is no Hagedorn temperature, so that the partition function is well defined at any positive temperature. All results are compared with the analogue results in anti--de Sitter spacetime, which is a nonconformal invariant background. Conformal invariance simplifies the mathematics of the problem but the physics remains mainly unchanged. Differences between conformal and non-conformal backgrounds only appear in the intermediate region of the string spectrum, but these differences are minor. For low and high masses, the string mass spectra in conformal and non-conformal backgrounds are identical. Interestingly enough, conformal invariance fixes the value of the spacetime curvature to be $\ensuremath{-}69/(26{\ensuremath{\alpha}}^{\ensuremath{'}}).$

Building string field theory around non-conformal backgrounds

The main limitations of string field theory arise because its present formulation requires a background representing a classical solution, a background defined by a strictly conformally invariant theory. Here we sketch a construction for a gauge-invariant string field action around non-conformal backgrounds. The construction makes no reference to any conformal theory. Its two-dimensional field-theoretic aspect is based on a generalized BRST operator satisfying a set of Weyl descent equations. Its geometric aspect uses a complex of moduli spaces of two-dimensional Riemannian manifolds having ordinary punctures, and organized by the number of special punctures which goes from zero to infinity. In this complex there is a Batalin-Vilkovisky algebra that includes naturally the operator which adds one special puncture. We obtain a classical field equation that appears to relax the condition of conformal invariance usually taken to define classical string backgrounds.