We define and compute algebraically a "perturbative part" of protected sphere correlation functions in the M2 brane SCFTs. These correlation functions are expected to have a holographic description in terms of twisted, $Ω$-deformed M-theory. We uncover a hidden perturbative triality symmetry which supports this conjecture. We also discuss some variants of the setup, involving M2 branes at $A_k$ singularities and D3 branes with a transverse compact direction.
Holography principle imposes a stringent constraint on the scale of quantum gravity $M_*$ in brane-world scenarios, where all matter is confined on the brane. The thermodynamic entropy of astrophysical black holes and sub-horizon volumes during big bang nucleosynthesis exceed the relevant bounds unless $M_* > 10^{(4-6)}$ TeV, so a hierarchy relative to the weak scale is unavoidable. We discuss the implications for extra dimensions as well as holography.
In the twisted M-theory setting, various types of fusion of M2 and M5 branes induce coproducts between the algebra of operators on M2 branes and the algebra of operators on M5 branes. By doing a perturbative computation in the gravity side, which is captured by the 5d topological holomorphic $U(1)$ Chern-Simons theory, we reproduce the non-perturbative coproducts.
Recently, Verlinde noted a surprising similarity between Friedmann equation governing radiation dominated universe and Cardy's entropy formula in conformal field theory. In this note, we study a brane-universe filled with radiation and stiff-matter. We analyze Friedmann equation in this context and compare our results with Cardy's entropy formula.
We investigate holography on an (n-1)-dimensional brane embedded in a background of AdS black holes, in n-dimensional Gauss-Bonnet gravity. We demonstrate that for a critical brane near the AdS boundary, the Friedmann equation corresponds to that of the standard cosmology driven by a CFT dual to the AdS bulk. We show that there is no holographic description for non-critical branes, or when the brane is further away from the AdS boundary. We then derive a Cardy-Verlinde formula for the dual CFT on the critical brane near the boundary. This gives us insight into the remarkable correspondence bet…
Exact holography for cosmological branes in an AdS-Schwarzschild bulk was first introduced in hep-th/0204218. We extend this notion to include all co-dimension one branes moving in non-trivial bulk spacetimes. We use a covariant approach, and show that the bulk Weyl tensor projected on to the brane can always be traded in for "holographic" energy-momentum on the brane. More precisely, a brane moving in a non-maximally symmetric bulk has exactly the same geometry as a brane moving in a maximally symmetric bulk, so long as we include the holographic fields on the brane. This correspondence is ex…
We consider the brane-world in the holographic point of view. Bearing the realistic models in mind, the bulk massless scalar field is introduced. First of all, we find the constraint on the coupling of the scalar fields with the matter(not holographic CFT) on the brane. We show that the traceless part of the energy-momentum tensor of holographic CFT is a part of the bulk Weyl tensor. The trace part which comes from the trace-anomaly is corresponding to the $ρ^2$-term appeared in the generalized FRW equation in the brane-world.
We consider world-volume description of M2-branes ending on an M5-brane. The system can be described either as a solitonic solution of the M5-brane field equations or in terms of an effective string propagating in 6-dimensions. We show that the zeroth order scalar scattering amplitudes behave similarly in both pictures. The soliton solution appears to have a horizon-like throat region. Due to the underlying geometric structure of the M5-brane theory, modes propagating near the horizon are subject to a large red-shift. This allows one to define a decoupling limit and implies a holographic duali…
A few supergravity solutions representing configurations of NS5-branes admit exact conformal field theory (CFT) description. Deformations of these solutions should be described by exactly marginal operators of the corresponding theories. We briefly review the essentials of these constructions and present, as a new case, the operators responsible for turning on angular momentum.
We propose a new program for computing a certain integrand of scattering amplitudes of four-dimensional gauge theories which we call the \textit{form factor integrand}, starting from 6d holomorphic theories on twistor space. We show that the form factor integrands can be expressed as sums of products of 1.) correlators of a 2d chiral algebra, related to the algebra of asymptotic symmetries uncovered recently in the celestial holography program, and 2.) OPE coefficients of a 4d non-unitary CFT. We prove that conformal blocks of the chiral algebras are in one-to-one correspondence with local ope…
We revisit the idea that the quantum dynamics of open strings ending on $N$ D3-branes in the large $N$ limit can be described at large `t Hooft coupling by classical closed string theory in the background created by the D3-branes in asymptotically flat spacetime. We study the resulting thermodynamics and compute the Hagedorn temperature and other properties of the D3-brane worldvolume theory in this regime. We also consider the theory in which the D3-branes are replaced by negative branes and show that its thermodynamics is well behaved. We comment on the idea that this theory can be thought o…
We study three-dimensional superconformal field theories on wrapped M5-branes. Applying the gauge/gravity duality and the recently proposed 3d-3d relation, we deduce quantitative predictions for the perturbative free energy of a Chern-Simons theory on hyperbolic 3-space. Remarkably, the perturbative expansion is expected to terminate at two-loops in the large N limit. We check the correspondence numerically in a number of examples, and confirm the N^3 scaling with precise coefficients.
We consider the first subleading terms in the low-energy cross section for the absorption of dilaton partial waves by D3-branes. We demonstrate that these corrections, computed previously via supergravity, can be reproduced exactly in a worldvolume calculation using a deformation of N=4 SYM theory by a dimension eight chiral operator. The calculation does not depend on how the theory is regularized. This result provides another hint that holographic duality between the D3-brane worldvolume theory and the corresponding supergravity solution may be valid beyond the near horizon limit.
At a meson melting transition in holographic QCD, a weak turbulence of mesons was found with critical embeddings of probe D-branes in gravity duals. The turbulent mesons have a power-law energy distribution $\varepsilon_n \propto (ω_n)^α$ where $ω_n$ is the mass of the $n$-th excited resonance of the meson tower. In this paper, we find that the turbulence power $α$ is universal, irrespective of how the transition is driven, by numerically calculating the power in various static brane setups at criticality. We also find that the power $α$ depends only on the cone dimensions of the probe D-brane…
Some recent literature has examined the holographic-induced cosmology of a brane universe in the background of an anti-de Sitter-black hole geometry. In this regard, curved-brane scenarios have begun to receive considerable attention. Our current interest is in a formal discrepancy that exists between two such works by Padilla (hep-th/0111247) and Youm (hep-th/0111276). In particular, these authors have incorporated different values for a conformal factor that is used to relate the thermodynamics of the relevant (AdS bulk and CFT brane) spacetimes. After a more general review, we clarify this …
We analyse a simple example of a holographically dual pair in which we topologically twist both theories. The holography is based on the two-dimensional N=2 supersymmetric Liouville conformal field theory that defines a unitary bulk quantum supergravity theory in three-dimensional anti-de Sitter space. The supersymmetric version of three-dimensional Liouville quantum gravity allows for a topological twist on the boundary and in the bulk. We define the topological bulk supergravity theory in terms of twisted boundary conditions. We corroborate the duality by calculating the chiral configuration…
We study the non-equilibrium steady-state phase transition from probe brane holography in $z=2$ Schrödinger spacetime. Concerning differential conductivity, a phase transition could occur in the conductor state. Considering constant current operator as the external field and the conductivity as an order parameter, we derive scaling behavior of order parameter near the critical point. We explore the critical exponents of the non-equilibrium phase transition in two different Schrödinger spacetimes, which originated $1)$ from supergravity, and $2)$ from AdS blackhole in the light-cone coordinates…
In the background of a charged AdS dilaton black hole, we investigate the movement of a self-graviting 3-brane and relevant holographic effects as the brane move close to the AdS boundary. The induced metric on brane corresponds to an exact FLRW geometry, while the evolution of brane is determined by Israel junction condition and the effective Einstein field equation on brane together. When the brane approaches the AdS boundary, AdS/CFT correspondence implies that a radiation dominated FLRW-universe ($P=\frac{1}{3}ρ$) should be given. According to the holographic renormalization procedure, we …
Doubly-holographic models, also known as Karch-Randall brane worlds, have shown to be very useful for understanding recent developments around computing entropies in semi-classical gravity coupled to conformal matter. Although there cannot be a faithful bulk/brane dictionary, we show that there is a simple dictionary which relates brane fields to subleading coefficients of a near-brane expansion of bulk fields -- similar to the case of AdS/CFT. We use this dictionary to find a general formula for the leading order contribution to graviton masses in the $d$ dimensional Karch-Randall braneworld.
We consider Type IIB Neveu-Schwarz five-branes transverse to C^2/Z_n orbifolds and conjecture that string theory on the near horizon geometry is dual to the decoupled theory on the branes. We analyze the conformal field theory describing the near horizon region and the world volume non-critical string theory. The modular invariance consistency condition of string theory is exactly reproduced as the gauge anomaly cancellation condition in the little string theories. We comment on aspects of the holographic nature of this duality.
We find and study the gravity duals of the supersymmetric vacua of N=6 mass-deformed Chern-Simons-matter theory for M2-branes. The classical solution extends that of Lin, Lunin and Maldacena by introducing a Z_k quotient and discrete torsions. The gravity vacua perfectly map to the recently identified supersymmetric field theory vacua. We calculate the masses of BPS charged particles in the weakly coupled field theory, which agree with the classical open membrane analysis when both calculations are reliable. We also comment on how non-relativistic conformal symmetry is realized in our gravity …
M-theory on $AdS_7 \times S^4$ admits a description where the $AdS_7$ factor is constructed as a timelike Hopf fibration over a non-compact three dimensional complex projective space $\tilde{\mathbb{CP}}^3$. We consider the worldvolume theory for M5-branes at a fixed $\tilde{\mathbb{CP}}^3$ radius which, after reduction along the timelike fibre, is given by an $Ω$-deformed Yang-Mills theory with eight supercharges. Taking the radius to infinity then induces a classical RG flow. We construct the fixed point action which has an enhanced 24 supercharges and which can be understood as the $(2,0)$ …
We use large N duality to study brane/anti-brane configurations on a class of Calabi-Yau manifolds. With only branes present, the Calabi-Yau manifolds in question give rise to N=2 ADE quiver theories deformed by superpotential terms. We show that the large N duality conjecture of hep-th/0610249 reproduces correctly the known qualitative features of the brane/anti-brane physics. In the supersymmetric case, the gauge theories have Seiberg dualities which are represented as flops in the geometry. Moreover, the holographic dual geometry encodes the whole RG flow of the gauge theory. In the non-sup…
We study the large $N$ limit of twisted partition functions on $\mathcal{M}_{g,p}$, the $S^1$ bundle of degree $p$ over a Riemann surface of genus $g$, for 3D $\mathcal{N}=2$ superconformal field theories arising as low-energy limit of wrapped $N$ M5-branes on hyperbolic 3-manifold $M$. We study contributions from two Bethe vacua which correspond to two canonical irreducible $SL(N, \mathbb{C})$ flat connections on $M$ via 3D-3D correspondence. Using mathematical results on perturbtaive Chern-Simons invariants around the flat connections, we find universal expressions for the large $N$ twisted …
We show how Higgs phases at non-zero density can be described using a simple analytic method for gauge theories possessing a holographic dual. We introduce co-dimension one branes in a bottom-up gravity dual that are sources of form flux, such that the effective curvature radius is changed when the brane is crossed. This mimics the expected flow produced by color branes nucleating in a top-down model.
Gukov, Martinec, Moore and Strominger found that the D1-D5-D5' system with the D5-D5' angle at 45 degrees admits a deformation "rho" preserving supersymmetry. Under this deformation, the D5-branes and D5'-branes reconnect along a single special Lagrangian manifold. We construct the near-horizon limit of this brane setup (for which no supergravity solution is currently known), imposing the requisite symmetries perturbatively in the deformation rho. Reducing to the three-dimensional effective gauged supergravity, we compute the scalar potential and verify the presence of a deformation with the e…
We study supersymmetric intersections of NS5-, D6- and D8-branes in type IIA string theory. We focus on the supergravity description of this system and identify a "near horizon" limit in which we recover the recently classified supersymmetric seven-dimensional AdS solutions of massive type IIA supergravity. Using a consistent truncation to seven-dimensional gauged supergravity we construct a universal supersymmetric deformation of these AdS vacua. In the holographic dual six-dimensional (1,0) superconformal field theory this deformation describes a universal RG flow on the tensor branch of the…
Using supersymmetric localization we compute the free energy and BPS Wilson loop vacuum expectation values for planar maximally supersymmetric Yang-Mills theory on $S^d$ in the strong coupling limit for $2\leq d<6$. The same calculation can also be performed in supergravity using the recently found spherical brane solutions. We find excellent agreement between the two sets of results. This constitutes a non-trivial precision test of holography in a non-conformal setting. The free energy of maximal SYM on $S^6$ diverges in the strong coupling limit which might signify the onset of little string…
We construct a new class of black brane solutions in Einstein-Maxwell-dilaton (EMD) theory, which is characterized by two parameters $a,b$. Based on the obtained solutions, we make detailed analysis on the ground state in zero temperature limit and find that for many cases it exhibits the behavior of vanishing entropy density. We also find that the linear-T resistivity can be realized in a large region of temperature for the specific case of $a^2=1/3$, which is the Gubser-Rocha model dual to a ground state with vanishing entropy density. Moreover, for $a=1$ we analytically construct the black …
As an extension of the so-called BMN conjecture, we investigate the plane-wave limit for possible holographic connection between bulk string theories in non-conformal 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 fo…
We derive and test a novel holographic duality in the B-model topological string theory. The duality relates the B-model on certain Calabi-Yau three-folds to two-dimensional chiral algebras defined as gauged $βγ\,$ systems. The duality conjecturally captures a topological sector of more familiar $\mathrm{AdS}_5 / \mathrm{CFT}_4$ holographic dualities.
We argue that vacua of string theory which asymptote at weak coupling to linear dilaton backgrounds are holographic. The full string theory in such vacua is ``dual'' to a theory without gravity in fewer dimensions. The dual theory is generically not a local quantum field theory. Excitations of the string vacuum, which can be studied in the weak coupling region using worldsheet methods, give rise to observables in the dual theory. An interesting example is string theory in the near-horizon background of parallel NS5-branes, the CHS model, which is dual to the decoupled NS5-brane theory (``littl…
This thesis is devoted to studying two important aspects of braneworld physics: their cosmology and their holography. We examine the Einstein equations induced on a general $(n-2)$-brane of arbitrary tension, embedded in some $n$-dimensional bulk. The brane energy-momentum tensor enters these equations both linearly and quadratically. From the point of view of a homogeneous and isotropic brane we see quadratic deviations from the FRW equations of the standard cosmology. There is also a contribution from a bulk Weyl tensor. We study this in detail when the bulk is AdS-Schwarzschild or Reissner-…
Quantum geometry of twisted Wess--Zumino--Witten branes is formulated in the framework of twisted Reflection Equation Algebras. It is demonstrated how the representation theory of these algebras leads to the correct classification and localisation of branes. A semiclassical formula for quantised brane positions is derived and shown to be consistent with earlier string-theoretic analyses.
Gauge theories living on stacks of D7-branes are holographically related to IIB gravitational backgrounds with a varying axion-dilaton field (F-theory). The axion-dilaton field is generated by D7, O7 and D-instanton sources and can be written in terms of the chiral correlators of the eight dimensional gauge theory living on the D7-branes. Using localization techniques, we prove that the same correlators determine the gauge coupling of the four-dimensional N=2 supersymmetric SU(2) gauge theories living on the elementary D3-brane which probes the F-theory geometries.
In this paper, based on the principles of Gauge/gavity duality, we explore the field theory description of certain special class of strongly coupled hyperscaling violating QFTs in the presence of scalar deformations near the \textit{effective} dynamical scale ($ r_F $) of the theory. In the language of the AdS/CFT duality, the scalar deformations of the above type could be thought of as being sourced due to some massless scalar excitation in the bulk which explicitly break the $ SO(2) $ rotational invariance along the spatial directions of the brane. As a consequence of these deformations, it …
It has been recently debated whether a class of generalized uncertainty principles that include gravitational sources of error are compatible with the holographic principle in models with extra spatial dimensions. We had in fact shown elsewhere that the holographic scaling is lost when more than four space-time dimensions are present. However, we shall show here that the validity of the holographic counting can be maintained also in models with extra spatial dimensions, but at the intriguing price that the equivalence principle for a point-like source be violated and the inertial mass differ f…
The five-dimensional description of generalized Randall-Sundrum cosmology is mapped via holography to a generalization of the Starobinsky model. This provides a holographic dual description of the cosmological brane-bulk energy exchange processes studied previously. Some simple solutions are presented in four dimensions.
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 construct vortex loop operators in the three-dimensional N = 6 supersymmetric Chern-Simons theory recently constructed by Aharony, Bergman, Jafferis and Maldacena. These disorder loop operators are specified by a vortex-like singularity for the scalar and gauge fields along a one dimensional curve in spacetime. We identify the 1/2, 1/3 and 1/6 BPS loop operators in the Chern-Simons theory with excitations of M-theory corresponding to M2-branes ending along a curve on the boundary of AdS_4 x S^7/Z_k. The vortex loop operators can also be given a purely geometric description in terms of regul…
It is shown that the Berezinski-Kosterlitz-Thouless phase transition that has been found in D3-D5 brane systems with nonzero magnetic field and charge density can also be found by tuning an extra-dimensional magnetic flux. We find numerical solutions for the probe D5-brane embedding and discuss properties of the solutions. We also demonstrate that the nontrivial embeddings include those which can be regarded as spontaneously breaking chiral symmetry.
We analyze the level-rank duality of omega_c-twisted D-branes of SU(N)_K (when N and K>2). When N or K is even, the duality map involves Z_2-cominimal equivalence classes of twisted D-branes. We prove the duality of the spectrum of an open string stretched between omega_c-twisted D-branes, and ascertain the relation between the charges of level-rank-dual omega_c-twisted D-branes.
We investigate the gauge/gravity duality between the ${\cal N} = 6$ mass-deformed ABJM theory with U$_k(N)\times$U$_{-k}(N)$ gauge symmetry and the 11-dimensional supergravity on LLM geometries with SO(2,1)$\times$SO(4)/${\mathbb Z}_k$ $\times$SO(4)/${\mathbb Z}_k$ isometry, in terms of a KK holography, which involves quadratic order field redefinitions. As a non-trivial extension of the previous work arXiv:1612.05066, we implement the KK mappings for various gauge invariant fields up to quadratic order to obtain 4-dimensional gravity fields. The non-linearity of the KK maps indicates that, in…
Level-rank duality of untwisted and twisted D-branes of WZW models is explored. We derive the relation between D0-brane charges of level-rank dual untwisted D-branes of su(N)_K and sp(n)_k, and of level-rank dual twisted D-branes of su(2n+1)_2k+1. The analysis of level-rank duality of twisted D-branes of su(2n+1)_2k+1 is facilitated by their close relation to untwisted D-branes of sp(n)_k. We also demonstrate level-rank duality of the spectrum of an open string stretched between untwisted or twisted D-branes in each of these cases.
The charges of the twisted D-branes of certain WZW models are determined. The twisted D-branes are labelled by twisted representations of the affine algebra, and their charge is simply the ground state multiplicity of the twisted representation. It is shown that the resulting charge group is isomorphic to the charge group of the untwisted branes, as had been anticipated from a K-theory calculation. Our arguments rely on a number of non-trivial Lie theoretic identities.
We study M/D-branes in a null-brane background. By taking a near horizon limit, one is left with cosmological models in the corresponding Poincaré patches. To deal with their usual horizons, we either extend these models to global AdS or remain in the Poincaré patch and apply a T-duality transformation whenever the effective radius of the compact dimension associated with the null-brane probes distances smaller than the string scale. The first scenario gives rise to null orbifolds in AdS spaces, which are described in detail. Their conformal boundaries are singular. The second has a dual gauge…
We study the Kaluza-Klein reduction of various $6d$ holomorphic theories. The KK reduction is analyzed in the BV formalism, resulting in theories that come from the holomorphic topological twist of $3d$ $\mathcal{N} = 2$ supersymmetric field theories. Effective interactions of the KK theories at the classical level can be obtained at all orders using homotopy transfer theorem. We also analyze a deformation of the theories that comes from deforming the spacetime geometry to $SL_2(\mathbb{C})$ due to the brane back-reaction. We study the boundary chiral algebras for the various KK theories. Usin…
We discuss the cosmological implications and the holographic dual theory of the 7D Randall-Sundrum (RS) gravitational set-up. Adding generic matter in the bulk on the 7D gravity side we study the cosmological evolution inferred by the non vanishing value of the brane-bulk energy exchange parameter. This analysis is achieved in detail for specific assumptions on the internal space evolution, including analytical considerations and numerical results. The dual theory is then constructed, making use of the holographic renormalization procedure. The resulting renormalized 6D CFT is anomalous and co…
The decoupling limit of a certain configuration of D3 branes in a Melvin universe defines a sector of string theory known as Puff Field Theory (PFT) - a theory with non-local dynamics but without gravity. In this work, we present a systematic analysis of the non-local states of strongly coupled PFT using gravitational holography. And we are led to a remarkable new holographic dictionary. We show that the theory admits states that may be viewed as brane protrusions from the D3 brane worldvolume. The footprint of a protrusion has finite size - the scale of non-locality in the PFT - and correspon…
The charges of the twisted branes for strings on the group manifold SU(n)/Z_d are determined. To this end we derive explicit (and remarkably simple) formulae for the relevant NIM-rep coefficients. The charge groups of the twisted and untwisted branes are compared and found to agree for the cases we consider.
For supergavrity solutions which are the product of an anti-de Sitter space with an Einstein space X, we study the relation between the amount of supersymmetry preserved and the geometry of X. Depending on the dimension and the amount of supersymmetry, the following geometries for X are possible, in addition to the maximally supersymmetric spherical geometry: Einstein-Sasaki in dimension 2k+1, 3-Sasaki in dimension 4k+3, 7-dimensional manifolds of weak G_2 holonomy and 6-dimensional nearly Kaehler manifolds. Many new examples of such manifolds are presented which are not homogeneous and have e…
