We use holographic correspondence to study transport of the conformal plasma in ${\mathbb R}^{2,1}$ in a phase with a spontaneously broken global $Z_2$ symmetry. The dual black branes in a Poincare patch of asymptotically $AdS_4$ have "hair" -- a condensate of the order parameter for the broken symmetry. This hair affects both the hydrodynamic and the nonhydrodynamic quasinormal modes of the black branes. Nonetheless, the shear viscosity of the conformal order is universal, the bulk viscosity vanishes and the speed of the sound waves is $c_s^2=\frac 12$. We compute the low-lying spectrum of the non-hydrodynamic modes. We identify a quasinormal mode associated with the fluctuations of the $Z_2$ order parameter with the positive imaginary part. The presence of this mode in the spectrum renders the holographic conformal order perturbatively unstable. Correspondingly, the dual black branes violate the correlated stability conjecture.
The purpose of this article is to present a short review of local conformal symmetry in curved 4d space-time. Furthermore we discuss the conformal anomaly and anomaly-induced effective actions. Despite the conformal symmetry is always broken at quantum level, it may be a basis of useful and interesting approximations for investigating quantum corrections.
By using a classical Liouville-type model of two dimensional dilaton gravity we show that the one-loop theory implies that the fate of a black hole depends on the conformal frame. There is one frame for which the evaporation process never stops and another one leading to a complete disappearance of the black hole. This can be seen as a consequence of the fact that thermodynamic variables are not conformally invariant. In the second case the evaporation always produces the same static and regular end-point geometry, irrespective of the initial state.
The free Schroedinger theory in d space dimensions is a non-relativistic conformal field theory. The interacting non-linear theory preserves this symmetry in specific numbers of dimensions at the classical (tree) level. This holds in particular for the Phi^4-theory in d = 2. We compute the full quantum corrections to the 4-point function to show that the symmetry is broken by an anomalous contribution proportional to the exact beta-function
It is observed that the Hidden Local Symmetry (HLS) for the vector mesons in the ordinary QCD with smaller N_f plays the role of the "Higgsed magnetic gauge symmetry" for the Seiberg duality in the SUSY QCD. For large N_f where the conformal phase transition with chiral restoration and deconfinement is expected to take place, we find that the HLS model also exhibits the chiral restoration by the loop corrections (including the quadratic divergence) in a manner similar to that in the CP^{N-1} model, provided that the bare HLS Lagrangian respects the Georgi's vector limit at a certain N_f (\appr…
We study the fate of a localized wavepacket in a classical conformal field theory with attractive interaction V(phi) = -lambda/4 phi^4. As potential is unbounded from below, homogeneous field collapses to singularity in finite time. However, finite size wavepacket can disperse before it collapses. Competition between the two outcomes results in a critical behavior, much like the one seen in gravitational collapse. We calculate the critical exponents, and show that there are static regular soliton-like solutions in the theory.
We study certain six dimensional theories arising on $(p,q)$ brane webs living on $\mathbb{R}\times S^1$. These brane webs are dual to toric elliptically fibered Calabi-Yau threefolds. The compactification of the space on which the brane web lives leads to a deformation of the partition functions equivalent to the elliptic deformation of the Ding-Iohara algebra. We compute the elliptic version Dotsenko-Fateev integrals and show that they reproduce the instanton counting of the six dimensional theory.
We review some aspects of the AdS supergravity description of RG flows. The case of a flow to an IR CFT can be rigorously studied within the framework of supergravity. Here we discuss various central charges of the conformal theory (included the usually neglected ones) and we compare them with QFT expectations. The case of flows to non-conformal theories is more problematic in that one usually encounters a naked singularity. We mainly focus on the flow to an IR N=1 super Yang-Mills theory. We discuss the properties of the solution and we briefly comment on the fate of the singularity. We also …
This paper addresses the fate of extended space-time symmetries, in particular conformal symmetry and supersymmetry, in two-dimensional Rindler space-time appropriate to a uniformly accelerated non-inertial frame in flat 1+1-dimensional space-time. Generically, in addition to a conformal co-ordinate transformation, the transformation of fields from Minkowski to Rindler space is accompanied by local conformal and Lorentz transformations of the components, which also affect the Bogoliubov transformations between the associated Fock spaces. I construct these transformations for massless scalars a…
We investigate the high temperature fate of four dimensional gauge-Yukawa theories featuring short distance conformality of either interacting or non-interacting nature. The latter is known as complete asymptotic freedom and, as templates, we consider non-abelian gauge theories featuring either two singlet scalars coupled to gauged fermions via Yukawa interactions or two gauged scalars with(out) fermions. For theories with interacting fixed points at short distance, known as asymptotically safe, we consider two calculable examples. Exploring the landscape of safe and free theories above we dis…
We argue that the Born-Infeld solution on the D$9-$brane is unstable under inclusion of derivative corrections to Born-Infeld theory coming from string theory. More specifically, we find no electrostatic solutions to the first order corrected Born-Infeld theory on the D$9-$brane which give a finite value for the Lagrangian.
We study the quantum dynamics of the Lemaître-Tolman-Bondi space-times using a polymer quantization prescription based on loop quantum cosmology that incorporates fundamental discreteness. By solving an effective equation derived from this quantization, we find analytical solutions for the Oppenheimer-Snyder and thin-shell collapse models, and numerical solutions for a variety of asymptotically flat collapsing dust profiles. Our study (i) tracks the formation, evolution and disappearance of dynamical horizons, (ii) shows that matter undergoes a non-singular bounce that results in an outgoing s…
In this work we investigate the effects of the Gribov prescription to get rid of zero-modes of the Faddeev-Popov operator, at one-loop order in perturbation theory, in the Landau-DeWitt gauge. Quantum fluctuations are taken around a transverse background gauge field. The one-loop effective action is explicitly computed, and the behavior of the gauge and ghost fields propagators are carefully investigated. At one-loop and for generic transverse background configurations the effective action is found to be \textit{not} background invariant, as expected, due to a non-vanishing background contribu…
We exhibit bound states in the spectrum of non-compact D-branes in N=2 Liouville conformal field theory. We interpret these states in the study of D-branes in the near-horizon limit of Neveu-Schwarz five-branes spread on a topologically trivial circle. We match semi-classical di-electric and repulsion effects with exact conformal field theory results and describe the fate of D-branes hitting NS5-branes. We also show that the bound states can give rise to massless vector and hyper multiplets in a low-energy gauge theory on D-branes deep inside the throat.
Analytic approximations to and numerical results for the semi-classical stress-energy tensor outside the horizon of a Schwarzschild black hole obtained in the 1980's and 1990's are re-examined in order to better understand the origin of Hawking radiation and the implications for the black hole information paradox. Polynomial fits to the numerical results for the tangential stress in 4D are obtained for conformally coupled spin 0 and spin 1 fields in the Hartle-Hawking and Unruh quantum states. What these results show is that the origin of the Hawking radiation is not pair creation or tunneling…
It was shown in arXiv:0810.4094 [hep-th] that in the presence of the magnetic field the sound waves in (2+1) dimensional plasma disappear and are replaces by a diffusive mode. Similarly, the shear and charge diffusion fluctuations form a subdiffusive mode. However, since the limit of small magnetic field does not commute with the hydrodynamic limit it is not obvious whether or not these modes are stable under higher order corrections. Using AdS/CFT correspondence we show that in the case of M2-brane plasma these modes do exist as we find the corresponding supergravity solutions. This allowed u…
The holographic principle relates (classical) gravitational waves in the bulk to quantum fluctuations and the Weyl anomaly of a conformal field theory on the boundary (the brane). One can thus argue that linear perturbations in the bulk of static black holes located on the brane be related to the Hawking flux and that (brane-world) black holes are therefore unstable. We try to gain some information on such instability from established knowledge of the Hawking radiation on the brane. In this context, the well-known trace anomaly is used as a measure of both the validity of the holographic pictu…
Relationships between gauge, conformal and discrete symmetries in particle physics are analysed. We study also the effect of the electroweak mixing on the cancellation of SU(2) anomalous actions. It is shown that the relation theta_{W} = 2(theta_{12}+theta_{23}+theta_{13}) between the Weinberg angle and the Cabibbo-Kobayashi-Maskawa angles should be satisfied and this effect is completely defined by the mixing of Dirac fermions. We compare two mechanisms of the spontaneous breaking of gauge symmetry, discuss the renormalizability of theories, and argue for the existence of the Majorana fermion…
We study the fate of reparametrization invariance of Wilson loops, also known as 'zig-zag' symmetry, under the RG flow using some simple cases as guidance. We restrict our analysis to large-$N$, strongly coupled CFTs and use the holographic dual description of a Wilson loop as a fundamental string embedded in asymptotically AdS spaces, at zero and nonzero temperature. We then introduce a cutoff in the holographic radial direction and integrate out the the section of the string closer to the AdS boundary in the spirit of holographic Wilsonian renormalization. We make explicit the map between Wi…
A parafermionic conformal theory with the symmetry Z_5 is constructed, based on the second solution of Fateev-Zamolodchikov for the corresponding parafermionic chiral algebra. The primary operators of the theory, which are the singlet, doublet 1, doublet 2, and disorder operators, are found to be accommodated by the weight lattice of the classical Lie algebra B_2. The finite Kac tables for unitary theories are defined and the formula for the conformal dimensions of primary operators is given.
Black hole entropy remains a deep puzzle: where does such enormous amount of entropy come from? Curiously, there exist gravitational configurations that possess even larger entropy than a black hole of the same mass, in fact, arbitrarily high entropy. These are the so-called monsters, which are problematic to the Anti-de Sitter/Conformal Field Theory (AdS/CFT) correspondence paradigm since there is far insufficient degrees of freedom on the field theory side to account for the enormous entropy of monsters in AdS bulk. The physics of the bulk however may be considerably modified at semi-classic…
We construct two-dimensional conformal field theories with a Z_N symmetry, based on the second solution of Fateev-Zamolodchikov for the parafermionic chiral algebra. Primary operators are classified according to their transformation properties under the dihedral group (Z_N x Z_2, where Z_2 stands for the Z_N charge conjugation), as singlets, [(N-1)/2] different doublets, and a disorder operator. In an assumed Coulomb gas scenario, the corresponding vertex operators are accommodated by the Kac table based on the weight lattice of the Lie algebra B_{(N-1)/2} when N is odd, and D_{N/2} when N is …
It has been recently shown that the presence of topological frustration, induced by periodic boundary conditions in an antiferromagnetic $XY$ chain made of an odd number of spins, prevents the realization of a perfectly staggered local order. Starting from this result and exploiting a recently introduced approach which enables the direct calculation of the expectation value of any operator with support over a finite range of lattice sites, in this work we investigate the possible fates of local orders. We show that, regardless of the variety of possible situations, they can be all arranged in …
Using the holographic correspondence as a tool, we study the dynamics of first-order phase transitions in strongly coupled gauge theories at finite temperature. Considering an evolution from the large to the small temperature phase, we compute the nucleation rate of bubbles of true vacuum in the metastable phase. For this purpose, we find the relevant configurations (bounces) interpolating between the vacua and we compute the related effective actions. We start by revisiting the compact Randall-Sundrum model at high temperature. Using holographic renormalization, we compute the kinetic term in…
The presence of a horizon is the principal marker for black holes as they appear in the classical theory of gravity. In General Relativity (GR), horizons have several defining properties. First, there exists a static spherically symmetric solution to vacuum Einstein equations which possesses a horizon defined as a null-surface on which the time-like Killing vector becomes null. Second, in GR, a co-dimension two sphere of minimal area is necessarily a horizon. On a quantum level, the classical gravitational action is supplemented by the quantum effective action obtained by integrating out the q…
Thermalisation of configurations with initial white noise power spectrum is studied in numerical simulations of a classical one-component $Φ^4$ theory in 2+1 dimensions, coupled to a small amplitude homogenous external field. The study is performed for energy densities corresponding to the broken symmetry phase of the system in equilibrium. The effective equation of the order parameter motion is reconstructed from its trajectory which starts from an initial value near the metastable point and ends in the stable ground state. This phenomenological theory quantitatively accounts for the decay of…
Black branes are studied in Einstein-Gauss-Bonnet (EGB) gravity. Evaporation drives black branes towards one of two singularities depending on the sign of $α$, the Gauss-Bonnet coupling. For positive $α$ and sufficiently large ratio $\sqrtα/L$, where $L/2π$ is the radius of compactification, black branes avoid the Gregory-Laflamme (GL) instability before reaching a critical state. No black branes with the radius of horizon smaller than the critical value can exist. Approaching the critical state branes have a nonzero Hawking temperature. For negative $α$ all black branes encounter the GL insta…
The first-order nature of the chiral phase transition in QCD-like theories can play crucial roles to address a dark side of the Universe, where the created out-of equilibrium is essential to serve as cosmological and astrophysical probes such as gravitational wave productions, which have extensively been explored. This interdisciplinary physics is built based on a widely-accepted conjecture that the thermal chiral phase transition in QCD-like theories with massless (light) three flavors is of first order. We find that such a first order feature may not hold, when ordinary or dark quarks are ex…
General Relativity is known to break down at singularities. However, it is expected that quantum corrections become important when the curvature is of the order of Planck scale avoiding the singularity. By calculating the effect of tidal forces on a freely falling inertial frame, and assuming the least possible size of the frame to be of the Planck length, we show that the Lorentz frames cease to exist at a finite distance from the singularity. Within that characteristic radius, one cannot apply General Relativity nor Quantum Field Theory as we know them today. Additionally we consider other q…
When a black hole evaporates, there arises a net energy flow from black hole into its outside environment (heat bath). The existence of energy flow means that the thermodynamic state of the whole system, which consists of the black hole and the heat bath, is in a nonequilibrium state. Therefore, in order to study the detail of evaporation process, the nonequilibrium effects of the energy flow should be taken into account. Using the nonequilibrium thermodynamics which has been formulated recently, this paper shows the following: (1) Time scale of black hole evaporation in a heat bath becomes sh…
The purpose of this paper is twofold. Firstly, we study the dynamical density fluctuations around the critical point(CP) of Quantum Chromodynamics(QCD) using dissipative relativistic fluid dynamics in which the coupling of the density fluctuations to those of other conserved quantities is taken into account. We show that the sound mode which is directly coupled to the mechanical density fluctuation is attenuated and in turn the thermal mode becomes the genuine soft mode at the QCD CP. We give a speculation on the possible fate of a Mach cone in the vicinity of the QCD CP as a signal of the exi…
We argue that in an inflationary cosmology a consequence of the lack of time translational invariance is that spontaneous breaking of a continuous symmetry and Goldstone's theorem \emph{do not} imply the existence of \emph{massless} Goldstone modes. We study spontaneous symmetry breaking in an O(2) model, and implications for O(N) in de Sitter space time. The Goldstone mode acquires a radiatively generated mass as a consequence of infrared divergences, and the continuous symmetry is spontaneously broken for any finite $N$, however there is a \emph{first order phase transition} as a function of…
