We study string theory duals of the expanding boost invariant conformal gauge theory plasmas at strong coupling. The dual supergravity background is constructed as an asymptotic late-time expansion, corresponding to equilibration of the gauge theory plasma. The absence of curvature singularities in the first few orders of the late-time expansion of the dual gravitational background unambiguously determines the equilibrium equation of the state, and the shear viscosity of the gauge theory plasma. While the absence of the leading pole singularities in the gravitational curvature invariants at the third order in late-time expansion determines the relaxation time of the plasma, the subleading logarithmic singularity can not be canceled within a supergravity approximation. We comment on the possible interpretations of this singularity.
In this article we summarise the brane solutions (instantons, black holes and strings) in 4 dimensions when embedded in N=2 supergravity. Like in 10 dimensions these solutions are related by duality transformations (T-duality, c-map). For the case that the graviphoton has no magnetic charge, we discuss the conformal field theory description of the near-horizon geometry. The decoupling of the massless modes in the matrix limit of the M-theory compactified on a Calabi-Yau threefold is discussed.
AdS/CFT duality is a conjectured dual correspondence between the large $N$ limit of Conformal Field Theory (CFT) in $d$-dimensions and the supergravity (SUGRA) in $d+1$-dimensional Anti de Sitter (AdS) space. By using this conjecture, we can study various properties of large $N$ CFT by simple calculations in SUGRA. Recently much attention has been paid to the Renormalization Group (RG) flow viewed from the SUGRA side. Such RG flow in CFT is known to be characterized by the c-function which connects CFTs with different central charges. Therefore, we are interested in deriving this c-function fr…
We reinterpret the Scherk-Schwarz (SS) boundary condition for SU(2)_R in a compactified five-dimensional (5D) Poincare supergravity in terms of the twisted SU(2)_U gauge fixing in 5D conformal supergravity. In such translation, only the compensator hypermultiplet is relevant to the SS twist, and various properties of the SS mechanism can be easily understood. Especially we show the equivalence between the SS twist and boundary constant superpotentials at the full supergravity level.
We explore the embedding of the phenomenological holographic models describing thermal relativistic ordered conformal phases in ${\mathbb R}^{2,1}$ in SUGRA/String theory. The dual black branes in a Poincare patch of asymptotically $AdS_4$ have ``hair'' -- a condensate of the order parameter for the broken symmetry. In a gravitational dual the order parameter for a spontaneous symmetry breaking is represented by a bulk scalar field with a nontrivial potential. To construct the ordered conformal phases perturbatively we introduce a phenomenological deformation parameter in the scalar potential.…
The conformal compensator formalism is a convenient and versatile representation of supergravity (SUGRA) obtained by gauge fixing conformal SUGRA. Unfortunately, practical calculations often require cumbersome manipulations of component field terms involving the full gravity multiplet. In this paper, we derive an alternative gauge fixing for conformal SUGRA which decouples these gravity complications from SUGRA computations. This yields a simplified tree-level action for the matter fields in SUGRA which can be expressed compactly in terms of superfields and a modified conformal compensator. Ph…
We shortly review our new superfield formalism in the framework of Fujita, Kugo, Ohashi 5D conformal supergravity, in particular with an $S^1/Z_2$ orbifold. The radion of the fifth dimension is embedded in two related superfields, a chiral and a general multiplet and is linked to the radion superfield of rigid SUSY. The superspace action of the gauge sector is of the Chern-Simons type. We also present the superspace action for hypermultiplets and discuss the role of compensators. The presented formalism should be very useful for applications. We demonstrate this for obtaining the RS solution.
We propose that the radion chiral supermultiplet of five dimensional compactified supergravity is obtained by reduction of the graviphoton gauge multiplet to N=1 superfields in the off shell 5D superconformal gravity formalism of Fujita, Kugo and Ohashi. We present a superfield Lagrangian of Chern-Simons type (similar to global SUSY), which reproduces all component couplings of gauge fields and the radion. A hypermultiplet superspace action is also proposed which correctly accounts for the coupling of matter multiplets with gauge and radion superfields. 4D supergravity enters by the coupling t…
We present a detailed study of radion stabilization within 5D conformal SUGRA compactified on an $S^{(1)}/Z_2$ orbifold. We use an effective 4D superfield description developed in our previous work. The effects of tree level bulk and boundary couplings, and in particular of one loop contributions and of a non perturbative correction on the radion stabilization are investigated. We find new examples of radion stabilization in non SUSY and (meta-stable) SUSY preserving Minkowski vacua.
In the context of a conformal Supergravity (SUGRA) model in the Einstein frame, in which the (next to) minimal supersymmetric standard model can embedded naturally to produce chaotic inflation scenarios, we study properties of gravitino in the cases where it is stable or unstable. In the latter case, we demonstrate that for large dilaton scale factors there is an enhanced magnitude of the gravitino width, when it decays to neutralino dark matter, as compared with the standard SUGRA case. In this context, we discuss the associated consequences as far as Big Bang Nucleosynthesis constraints and …
We address some issues related to the construction of general Kaluza-Klein (KK) ansätze for the compactification of a supergravity (sugra) theory on a sphere $S_m$. We first reproduce various ansätze for compactification to 7d from the ansatz for the full nonlinear KK reduction of 11d sugra on $AdS_7\times S_4$. As a side result, we obtain a lagrangian formulation of 7d ${\cal N}=2$ gauged sugra, which so far had only a on-shell formulation, through field equations and constraints. The $AdS_7\times S_4$ ansatz generalizes therefore all previous sphere compactifications to 7d. Then we consider …
Motivated by recent cosmological observations of a possibly unsuppressed primordial tensor component $r$ of inflationary perturbations, we reanalyse in detail the 5D conformal SUGRA originated natural inflation model of Ref. [1]. The model is a supersymmetric variant of 5D extra natural inflation, also based on a shift symmetry, and leads to the potential of natural inflation. Coupling the bulk fields generating the inflaton potential via a gauge coupling to the inflaton with brane SM states we necessarily obtain a very slow gauge inflaton decay rate and a very low reheating temperature $T_r\s…
Generalizing our previous work, we show how $O(d,d)$ transformations can be used to "boost away" in new dimensions the physical singularities that occur generically in cosmological and/or black-hole string backgrounds. As an example, we show how a recent model by Nappi and Witten can be made singularity-free via $O(3,3)$ boosts involving a fifth dimension.
The Operator Product Expansion is a useful tool to represent correlation functions. In this note we extend Conformal Regge theory to provide an exact OPE representation of Lorenzian four-point correlators in conformal field theory, valid even away from Regge limit. The representation extends convergence of the OPE by rewriting it as a double integral over continuous spins and dimensions, and features a novel "Regge block". We test the formula in the conformal fishnet theory, where exact results involving nontrivial Regge trajectories are available.
We study string theory duals of the expanding boost invariant conformal gauge theory plasmas at strong coupling. The dual supergravity background is constructed as an asymptotic late-time expansion, corresponding to equilibration of the gauge theory plasma. The absence of curvature singularities in the first few orders of the late-time expansion of the dual gravitational background unambiguously determines the equilibrium equation of the state, and the shear viscosity of the gauge theory plasma. While the absence of the leading pole singularities in the gravitational curvature invariants at th…
Conformal Field Theories (CFTs) have rich dynamics in heavy states. We describe the constraints due to spontaneously broken boost and dilatation symmetries in such states. The spontaneously broken boost symmetries require the existence of new low-lying primaries whose scaling dimension gap, we argue, scales as $O(1)$. We demonstrate these ideas in various states, including fluid, superfluid, mean field theory, and Fermi surface states. We end with some remarks about the large charge limit in 2d and discuss a theory of a single compact boson with an arbitrary conformal anomaly.
We present a detailed study of the reduction to 4D of 5D supergravity compactified on the S^1/Z_2 orbifold. For this purpose we develop and employ a recently proposed N=1 conformal superfield description of the 5D supergravity couplings to abelian vector and hypermultiplets. In particular, we obtain a unique relation of the "radion" to chiral superfields as in global 5D SUSY and we can embed the universal hypermultiplet into this formalism. In our approach, it is transparent how the superconformal structure of the effective 4D actions is inherited from the one of the original 5D supergravity. …
Proposals that $O(d,d)$ boosts of trivial backgrounds lead to non-trivial conformally invariant backgrounds are checked to two loop order. We find that conformal invariance can be achieved by adding simple higher order corrections to the metric and dilaton.
We compute finite coupling correction to a nonlinear second order hydrodynamic coefficient in the boost invariant expansion of the N=4 supersymmetric Yang-Mills plasma. The result is universal for a large class of strongly coupled four dimensional conformal gauge theories.
Bosonic Bogoliubov transformations as Lorentz boosts in $(c,{\overline c})=(1,1)$ conformal field theories with marginal $J{\overline J }$ deformations
Conformal totally symmetric arbitrary spin bosonic fields in flat space-time of even dimension greater than or equal to four are studied. Second-derivative (ordinary-derivative) formulation for such fields is developed. We obtain gauge invariant Lagrangian and the corresponding gauge transformations. Gauge symmetries are realized by involving the Stueckelberg and auxiliary fields. Realization of global conformal boost symmetries on conformal gauge fields is obtained. Modified de Donder gauge condition and de Donder-Stueckelberg gauge condition are introduced. Using the de Donder-Stueckelberg g…
We determine analytically the dependence of the approach to thermal equilibrium of strongly coupled plasmas on the breaking of scale invariance. The theories we consider are the holographic duals to Einstein gravity coupled to a scalar with an exponential potential. The coefficient in the exponent, $X$, is the parameter that controls the deviation from the conformally invariant case. For these models we obtain analytic solutions for the plasma expansion in the late-time limit, under the assumption of boost-invariance, and we determine the scaling behaviour of the energy density, pressure, and …
Conformal fields in flat space-time of even dimension greater than or equal to four are studied. Second-derivative formulation for spin 0,1,2 conformal bosonic fields and first-derivative formulation for spin 1/2,3/2 conformal fermionic fields are developed. For the spin 1,3/2,2 conformal fields, we obtain gauge invariant Lagrangians and the corresponding gauge transformations. Gauge symmetries are realized by involving Stueckelberg fields and auxiliary fields. Realization of global conformal boost symmetries is obtained. Modified Lorentz and de Donder gauge conditions are introduced. Ordinary…
We consider a simple extension to the previously found gravity solution corresponding to a boost invariant Bjorken plasma, by allowing components that are asymmetric under parity flipping of the spacetime rapidity. Besides the question whether this may have a realization in collisions of different species of projectiles, such as lead-gold collision, our new time dependent gravity background can serve as a test ground for the recently proposed second order conformal viscous hydrodynamics. We find that non-trivial parity-asymmetric effects start to appear at second order in late time expansion, …
We extend our previous analysis of holographic heavy ion collisions in non-conformal theories. We provide a detailed description of our numerical code. We study collisions at different energies in gauge theories with different degrees of non-conformality. We compare four relaxation times: the hydrodynamization time (when hydrodynamics becomes applicable), the EoSization time (when the average pressure approaches its equilibrium value), the isotropization time (when the longitudinal and transverse pressures approach each other) and the condensate relaxation time (when the expectation value of a…
Conformal totally symmetric arbitrary spin currents and shadow fields in flat space-time of dimension greater than or equal to four are studied. Gauge invariant formulation for such currents and shadow fields is developed. Gauge symmetries are realized by involving the Stueckelberg fields. Realization of global conformal boost symmetries is obtained. Gauge invariant differential constraints for currents and shadow fields are obtained. AdS/CFT correspondence for currents and shadow fields and the respective normalizable and non-normalizable solutions of massless totally symmetric arbitrary spin…
We construct numerically the minimal surface in AdS spacetime surrounded by the light-like segments, which are dual to the 4, 6 and 8-point gluon scattering amplitudes in N=4 super Yang-Mills theory. We evaluate the area of the minimal surface in the radial cut-off regularization and compare these areas with the formula conjectured by Bern, Dixon and Smirnov (BDS), which is modified by the remainder function of cross-ratios of external momenta for n(\geq 6)-point amplitudes. In our momentum configuration cross-ratios are constant. We calculate the difference of areas with different conformal b…
We present some exact solutions to the ideal hydrodynamics of a relativistic superfluid with an almost-conformal equation of state. The solutions have stress tensors which are invariant under Lorentz boosts in one direction, and represent superfluid generalisations of the Bjorken and Gubser flows. We also study corrections to the flows in first-order hydrodynamics, arguing that dissipation is dominated by the shear viscosity. We present some simple numerical solutions for these viscous corrections. Finally, we estimate the size of corrections to the flows arising when the spontaneously broken …
Conformally compactified (3+1)-dimensional Minkowski spacetime may be identified with the projective light cone in (4+2)-dimensional spacetime. In the latter spacetime the special conformal group acts via rotations and boosts, and conformal inversion acts via reflection in a single coordinate. Hexaspherical coordinates facilitate dimensional reduction of Maxwell electromagnetic field strength tensors to (3+1) from (4 + 2) dimensions. Here we focus on the operation of conformal inversion in different coordinatizations, and write some useful equations. We then write a conformal invariant and a p…
From a gauge $SU(2,2|2)$ model with broken supersymmetry, we construct an action for $SU(2)\times U(1)$ Yang-Mills theory coupled to gravity and matter. The connection components for AdS boosts and special conformal translations are auxiliary fields and their fixing reduces the theory to two distintive sectors: a vector-like gauge theory with general relativity and a chiral gauge theory where gravity drops out. We discuss some of the main classical features of the model such as the predicted tree level gauge couplings, cosmological constant value, mass-like terms and the Einstein equations.
We analyse the global structure of time-dependent geometries dual to expanding plasmas, considering two examples: the boost invariant Bjorken flow, and the conformal soliton flow. While the geometry dual to the Bjorken flow is constructed in a perturbation expansion at late proper time, the conformal soliton flow has an exact dual (which corresponds to a Poincare patch of Schwarzschild-AdS). In particular, we discuss the position and area of event and apparent horizons in the two geometries. The conformal soliton geometry offers a sharp distinction between event and apparent horizon; whereas t…
We study the screening length L_s of a heavy quark-antiquark pair in strongly coupled gauge theory plasmas flowing at velocity v. Using the AdS/CFT correspondence we investigate, analytically, the screening length in the ultra-relativistic limit. We develop a procedure that allows us to find the scaling exponent for a large class of backgrounds. We find that for conformal theories the screening length is (boosted energy density)^{-1/d}. As examples of conformal backgrounds we study R-charged black holes and Schwarzschild-anti-deSitter black holes in (d+1)-dimensions. For non-conformal theories…
In the spirit of the AdS/CFT correspondence, we investigate the hydrodynamics of the dual conformal field in the Gauss-Bonnet gravity. By considering the parameters of the boosted black brane in the Gauss-Bonnet gravity as functions of boundary coordinates, and then solving the corresponding correction terms, we calculate the first order stress-energy tensor of the dual conformal field. From this first order stress-energy tensor, we also obtain the shear viscosity and entropy density. And these results are consistent with those of some previous works from the effective coupling of gravitons.
Boost-invariant dynamics of a strongly-coupled conformal plasma is studied in the regime of early proper-time using the AdS/CFT correspondence. It is shown, in contrast with the late-time expansion, that a scaling solution does not exist. The boundary dynamics in this regime depends on initial conditions encoded in the bulk behavior of a Fefferman-Graham metric coefficient at initial proper-time. The relation between the early-time expansion of the energy density and initial conditions in the bulk of AdS is provided. As a general result it is proven that a singularity of some metric coefficien…
In a recent paper [J. P. M. Pitelli, Phys. Rev. D {\bf 99}, 108701 (2019)], one of us showed that the vacuum state associated to conformal fields on a Poicaré patch of anti-de Sitter spacetime is not $\text{AdS}$ invariant for fields satisfying non-trivial boundary conditions (by non-trivial we mean neither Dirichlet nor Neumann) at the conformal boundary. In this way, two isometrically related observers in anti-de Sitter space have different notions of no particle content. Therefore, an observer who is suddenly transported to a different (but isometrically related) frame will feel a bath of p…
