Note on higher spins and holographic symmetry algebra
National Institute of Science Education and Research (NISER)（印度科学教育与研究国立研究所）；Homi Bhabha National Institute（霍米·巴巴国立研究所）；Indian Institute of Technology Ropar（印度技术学院罗帕尔分校）
Shamik Banerjee, Suman Guchait, Raju Mandal, Sudhakar Panda
In this paper we discuss a higher spin extension of the holographic symmetry algebra for graviton and gluon. Our primary observation is that in the presence of higher spin particles the soft symmetry algebra has a subalgebra isomorphic to $w_{\infty}$ which is generated by the \textit{conformally soft higher spin particles}. This $w_{\infty}$ subalgebra does not commute with the $w_{1+\infty}$ subalegbra generated by the conformally soft gravitons. The same thing holds for the colored higher spin particles. One gets a subalgebra isomorphic to the $S$-algebra which is generated by the conformally soft colored higher spin particles. We further verify the soft algebra for colored higher spin particles using the (tree-level) $4$-point MHV amplitude of the higher spin Yang-Mills theory constructed in arXiv:2210.07130. At the end we also discuss the higher spin extension of the deformed holographic symmetry algebra for non-zero cosmological constant as constructed in arXiv:2312.00876.
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The purpose of these lecture notes is to give a quick and introductory overview of holographic superconductors. Besides the actual description of the standard holographic superconductor, attention is paid to the motivations and the relation with the previous, non-holographic context.
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In this note, we study the effects of non-zero magnetic field on the fermion spectral function coupled with a non-minimal coupling in the background of a dyonic $AdS_4$ black hole. The system can be reduced to a non magnetic one with the momentum being quantized into Landau levels $n$. By tuning the coupling parameter, we study its effect on the Fermi level and the quasiparticle width. We found an interesting scaling relation between the decay width and the coupling parameter, with a universal scaling exponent which is independent of the levels $n$.
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We discuss the field theory interpretation (via holographic duality) of some recently-discovered string theory solutions with varying flux, focusing on four dimensional theories with N=2 supersymmetry and with N=1 supersymmetry which arise as the near-horizon limits of "fractional D3-branes". We argue that in the N=2 case the best interpretation of the varying flux in field theory is via a Higgs mechanism reducing the rank of the gauge group, and that there is no need to invoke a duality to explain the varying flux in this case. We discuss why a similar interpretation does not seem to apply to…
The volume inside a Ryu-Takayanagi surface has been conjectured to be related to the complexity of subregions of the boundary field theory. Here, we study the behaviour of this volume analytically, when the entangling surface has a strip geometry. We perform systematic expansions in the low and high temperature regimes for AdS-Schwarzschild and RN-AdS black holes. In the latter regime, we point out spurious divergences that might occur due to the limitations of a near horizon expansion. A similar analysis is performed for extremal black holes, and at large charge, we find that there might be s…
In this note we remark that the butterfly effect can be used to diagnose the phase transition of superconductivity in a holographic framework. Specifically, we compute the butterfly velocity in a charged black hole background as well as anisotropic backgrounds with Q-lattice structure. In both cases we find its derivative to the temperature is discontinuous at critical points. We also propose that the butterfly velocity can signalize the occurrence of thermal phase transition in general holographic models.
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This is a long-overdue companion paper to arXiv:1512.00073. We study the relation between $sl(3|2)$ Chern-Simons supergravity on AdS$_3$ and two-dimensional CFT's with $\mathcal{N}=2$ super-$\mathcal{W}_3$ symmetry. Specifically, we carry out a complete analysis of asymptotic symmetries in a basis that makes the superconformal structure transparent, allowing us to establish the precise dictionary between currents and transformation parameters in the bulk and their boundary counterparts. We also discuss the incorporation of sources and display in full detail the corresponding holographic Ward i…
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In our previous work (Phys. Rev. D63, 085010, hep-th/0011290), we showed that the brane universe on the giant graviton moving in the near-horizon background of the dilatonic D(6-p)-brane is described by the mirage cosmology. We study thermodynamic properties of the moving giant graviton by applying thermodynamics of cosmology and the recently proposed holographic principles of cosmology. We find that the Fischler-Susskind holographic bound is satisfied by the closed brane universe on the moving giant graviton with p>3. The Bekenstein and the Hubble entropy bounds and the recently proposed Verl…
We consider situations where the renormalized geometric entropy, as defined by the AdS/CFT ansatz of Ryu and Takayanagi, shows extensive behavior in the volume of the entangled region. In general, any holographic geometry that is `capped' in the infrared region is a candidate for extensivity provided the growth of minimal surfaces saturates at the capping region, and the induced metric at the `cap' is non-degenerate. Extensivity is well-known to occur for highly thermalized states. In this note, we show that the holographic ansatz predicts the persistence of the extensivity down to vanishing t…
We try to find a possible origin of the holographic principle in the Lorentz-covariant Yang's quantized space-time algebra (YSTA). YSTA, which is intrinsically equipped with short- and long-scale parameters, $λ$ and $R$, gives a finite number of spatial degrees of freedom for any bounded spatial region, providing a basis for divergence-free quantum field theory. Furthermore, it gives a definite kinematical reduction of spatial degrees of freedom, compared with the ordinary lattice space. On account of the latter fact, we find a certain kind of kinematical holographic relation in YSTA, which ma…
In this note we calculate the holographic entanglement entropy in the presence of a conformal interface for a geometric configuration in which the entangling region ${\cal A}$ lies on one side of the interface. For the supersymmetric Janus solution we find exact agreement between the holographic and CFT calculation of the entanglement entropy.
In this note, we have addressed various issues on zero temperature holographic superfluids. First, inspired by our numerical evidence for the equality between the superfluid density and particle density, we provide an elegant analytic proof for this equality by a boost trick. Second, using not only the frequency domain analysis but also the time domain analysis from numerical relativity, we identify the hydrodynamic normal modes and calculate out the sound speed, which is shown to increase with the chemical potential and saturate to the value predicted by the conformal field theory in the larg…
We present a simple derivation of an upper bound on the average size of the true vacuum bubbles at the end of inflation, in models of extended inflation type. The derivation uses the inequality that the total energy inside a given volume must be less than its linear dimensions. The above bound is the same as that obtained earlier, by applying the holographic principle according to Fischler-Susskind prescription. Such a bound leads to a lower bound on the denisty fluctuations.
We investigate systematically the effect of the nonlinear correction to the usual Maxwell electrodynamics on the holographic dual models in the backgrounds of AdS black hole and AdS soliton. Considering three types of typical nonlinear electrodynamics, we observe that in the black hole background the higher nonlinear electrodynamics correction makes the condensation harder to form and changes the expected relation in the gap frequency, which is similar to that caused by the curvature correction. However, in strong contrast to the influence of the curvature correction, we find that in the AdS s…
In this note we calculate susceptibilities, as derivatives of a thermodynamical potential, for the general perturbative holographic set-up for transport with magnetic field, charge density and topological term, and compare with the quantities obtained in the standard $AdS_4$ dyonic black hole analysis of Hartnoll and Kovtun. We find that the results do not match, despite previous expectations.
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We employ the matching method to analytically investigate the holographic superconductors with Lifshitz scaling in an external magnetic field. We discuss systematically the restricted conditions for the matching method and find that this analytic method is not always powerful to explore the effect of external magnetic field on the holographic superconductors unless the matching point is chosen in an appropriate range and the dynamical exponent $z$ satisfies the relation $z=d-1$ or $z=d-2$. From the analytic treatment, we observe that Lifshitz scaling can hinder the condensation to be formed, w…
All 4D gauge and gravitational theories in asymptotically flat spacetimes contain an infinite number of non-trivial symmetries. They can be succinctly characterized by generalized 2D currents acting on the celestial sphere. A complete classification of these symmetries and their algebras is an open problem. Here we construct two towers of such 2D currents from positive-helicity photons, gluons, or gravitons with integer conformal weights. These generate the symmetries associated to an infinite tower of conformally soft theorems. The current algebra commutators are explicitly derived from the p…
In the preceding paper, we derived a kind of kinematical holographic relation (KHR) in the Lorentz-covariant Yang's quantized space-time algebra (YSTA). It essentially reflects the fundamental nature of the noncommutative geometry of YSTA and its representation, that is, a definite kinematical reduction of spatial degrees of freedom in comparison with the ordinary lattice space. On the basis of the relation and its extension to various spatial dimensions, we derive a new area-entropy relation in a simple $D_0$ brane gas system subject to YSTA, following the idea of M-theory. Furthermore, we ma…
Notes on holographic renormalization as a tool for UV analysis and derivation of the two-point Ward identity encoding symmetry breaking. Goldstone theorem is reviewed, discussing in particular the modifications required by its extension to non-relativistic field theories. The Ward identity encoding both spontaneous and explicit breaking are derived by general principles. Holographic renormalization is presented in a quite operational fashion. The derivation of the Ward identity in holography is illustrated by an example.
Over the last few years a certain class of dark-energy models decaying inversely proportional to the square of the horizon distance emerged on the basis either of Heisenberg uncertainty relations or of the uncertainty relation between the four-volume and the cosmological constant. The very nature of these dark energies is understood to be the same, namely it is the energy of background space/metric fluctuations. Putting together these uncertainty relations one finds that the model of random fluctuations of the background metric is favored over the holographic one.
The present-day significance of Yang's quantized space-time algebra (YST) is pointed out from the holographic viewpoint. One finds that the D-dimensional YST and its modified version (MYST) have the background symmetry SO(D+1,1) and SO(D,2), which are well known to underlie the dS/CFT and AdS/CFT correspondences, respectively. This fact suggests a new possibility of dS/YST and AdS/MYST in parallel with dS/CFT and AdS/CFT, respectively. The spatial components of quantized space-time and momentum operators of YST have discrete eigenvalues and their respective minimums, $a$ and 1/R, without contr…
