82 pages, 1 figure; v2: JHEP version - expanded exposition and references, improved the discussion of contact effects; v3: corrected signs, in light of later work on boundary-local/twistor dictionary
We consider the holographic duality between type-A higher-spin gravity in AdS_4 and the free U(N) vector model. In the bulk, linearized solutions can be translated into twistor functions via the Penrose transform. We propose a holographic dual to this transform, which translates between twistor functions and CFT sources and operators. We present a twistorial expression for the partition function, which makes global higher-spin symmetry manifest, and appears to automatically include all necessary contact terms. In this picture, twistor space provides a fully nonlocal, gauge-invariant description underlying both bulk and boundary spacetime pictures. While the bulk theory is handled at the linear level, our formula for the partition function includes the effects of bulk interactions. Thus, the CFT is used to solve the bulk, with twistors as a language common to both. A key ingredient in our result is the study of ordinary spacetime symmetries within the fundamental representation of higher-spin algebra. The object that makes these "square root" spacetime symmetries manifest becomes the kernel of our boundary/twistor transform, while the original Penrose transform is identified as a "square root" of CPT.
We give a holographic argument in favor of the AdS Penrose inequality, which conjectures a lower bound on the total mass in terms of the area of apparent horizons. This inequality is often viewed as a test of cosmic censorship. We further find a connection between the area law for apparent horizons and the Penrose inequality. Finally, we show that the argument also applies to solutions with charge, resulting in a charged Penrose inequality in AdS.
The recent holographic deduction of Penrose inequality only assumes null energy condition while the weak or dominant energy condition is required in usual geometric proof. This paper makes a step toward filling up gap between these two approaches. For planar/spherically symmetrically asymptotically Schwarzschild anti-de Sitter (AdS) black holes, we give a purely geometric proof for Penrose inequality by assuming the null energy condition. We also point out that two naive generalizations of charged Penrose inequality are not generally true and propose two new candidates. When the spacetime is a…
We discuss the Penrose limit of pure AdS space, which is flat Minkowski space. Even though there is no holographic principle, we construct a ``holographic screen'' on which information on the corresponding CFT is encoded. The screen is obtained as a gauge-fixing condition upon restricting the Hilbert space to the states that are annihilated by the generator of scale transformations. This constraint leads to Dirac brackets which turn the Poincare algebra into the algebra of the conformal group on the ``holographic screen.''
We explore bosonic string sigma models on warped $ BTZ\times S^3 $ both in the plane wave as well as beyond plane wave limit. Using the light cone gauge, we obtain the corresponding Hamiltonian and therefore the spectrum associated with the pp wave strings. Our analysis reveals a constant shift in the spectrum arising as a result of TsT transformations along the isometries of the target space manifold. Imposing the energy positivity constraint on the CFT$_2 $ spectrum, we estimate an upper bound on the shift. We also estimate corrections as we go beyond the plane wave limit. Finally, we perfor…
In the Penrose limit, AdS*S space turns into a Cahen-Wallach (CW) space whose Killing vectors satisfy a Heisenberg algebra. This algebra is mapped onto the holographic screen on the boundary of AdS. I show that the Heisenberg algebra on the boundary of AdS may be obtained directly from the CW space by appropriately constraining the states defined on it. The transformations generated by the constraint are similar to gauge transformations. The ``holographic screen'' on the CW space is thus obtained as a ``gauge-fixing'' condition.
In three dimensions, a theory with spontaneous breaking of supersymmetry was described holographically by the Maldacena-Nastase (MNa) solution. We revisit the issue of its Penrose limit, and compare the resulting pp wave and its string eigenstates to a sector of the theory on 5-branes reduced on $S^3$, and a spin chain-like system. We obtain many of the features of the pp wave analysis, but a complete matching still eludes us. We suggest possible explanations for the resulting partial mismatch, and compare against other spin chains for 3-dimensional field theories with gravity duals.
We give a supersymmetric extension to the six-dimensional Penrose transform and give an integral formula for the on-shell (0, 2) supermultiplet. The relationship between super fields on space-time and twistor space is clarified and the space-time superfield constraint equations are derived from the geometry of supertwistor space. We also explain the extension to more general (0,n) supermultiplets and give twistor actions for these theories.
We obtain explicit realizations of holographic renormalization group (RG) flows from M-theory, from E^{2,1} \times Spin(7) at UV to AdS_4 \times \tilde{S^7} (squashed S^7) at IR, from E^{2,1} \times CY4 at UV to AdS_4 \times Q^{1,1,1} at IR, and from E^{2,1} \times HK (hyperKahler) at UV to AdS_4 \times N^{0,1,0} at IR. The dual type IIA string theory configurations correspond to D2-D6 brane systems where D6 branes wrap supersymmetric four-cycles. We also study the Penrose limits and obtain the pp-wave backgrounds for the above configurations. Besides, we study some examples of non-supersymmet…
The Penrose Transform and the Kerr-Schild double copy
SISSA（国际高等研究学院）；INFN Sezione di Trieste（意大利国家核物理研究所的里雅斯特分部）；IFPU - Institute for Fundamental Physics of the Universe（宇宙基础物理研究所）；Imperial College London（伦敦帝国理工学院）；Los Alamos National Laboratory（洛斯阿拉莫斯国家实验室）；Brown University（布朗大学）
We examine a stationary but non-static asymptotically AdS_3 spacetime with two causally connected conformal boundaries, each of which is a ``null cylinder'', namely a cylinder with a null direction identified. This spacetime arises from three different perspectives: (i) as a non-singular, causally regular orbifold of global AdS_3 by boosts, (ii) as a Penrose-like limit focusing on the horizon of extremal BTZ black holes, and (iii) as an S^1 fibration over AdS_2. Each of these perspectives sheds an interesting light on holography. Examination of the conformal boundary of the spacetime shows tha…
It was recently shown by Witten that B-type open topological string theory with the supertwistor space CP^{3|4} as a target space is equivalent to holomorphic Chern-Simons (hCS) theory on the same space. This hCS theory in turn is equivalent to self-dual N=4 super Yang-Mills (SYM) theory in four dimensions. We review the supertwistor description of self-dual and anti-self-dual N-extended SYM theory as the integrability of super Yang-Mills fields on complex (2|N)-dimensional superplanes and demonstrate the equivalence of this description to Witten's formulation. The equivalence of the field equ…
Recently, we introduced the "Newman-Penrose map," a novel correspondence between a certain class of solutions of Einstein's equations and self-dual solutions of the vacuum Maxwell equations, which we showed was closely related to the classical double copy. Here, we give an alternative definition of this correspondence in terms of quantities that are defined naturally on twistor space, and a shear-free null geodesic congruence on Minkowski space whose twistorial character is articulated by the Kerr theorem. The advantage of this reformulation is that it is purely geometrical in nature, being ma…
We generalize Penrose's notion of conformal infinity of spacetime, to situations with anisotropic scaling. This is relevant not only for Lifshitz-type anisotropic gravity models, but also in standard general relativity and string theory, for spacetimes exhibiting a natural asymptotic anisotropy. Examples include the Lifshitz and Schrodinger spaces (proposed as AdS/CFT duals of nonrelativistic field theories), warped AdS_3, and the near-horizon extreme Kerr geometry. The anisotropic conformal boundary appears crucial for resolving puzzles of holographic renormalization in such spacetimes.
The Penrose-Gueven limit simplifies a given supergravity solution into a pp-wave background. Aiming at clarifying its relation to renormalization group flow we study the Penrose-Guven limit of supergravity backgrounds that are dual to non-conformal gauge theories. The resulting backgrounds fall in a class simple enough that the quantum particle is exactly solvable. We propose a map between the effective time-dependent quantum mechanical problem and the RG flow in the gauge theory. As a testing ground we consider explicitly two Penrose limits of the infrared fixed point of the Pilch-Warner solu…
We study one and two point functions of conformal field theories on spaces of maximal symmetry with and without boundaries and investigate their spectral representations. Integral transforms are found, relating the spectral decomposition to renormalized position space correlators. Several applications are presented, including the holographic boundary CFTs as well as spacelike boundary CFTs, which provide realizations of the pseudo-conformal universe.
We study dual conformal transformations of minimal area surfaces in $AdS_5 \times S^5$ corresponding to holographic smooth Wilson loops and some other related observables. To act with dual conformal transformations we map the string solutions to the dual space by means of T-duality, then we apply a conformal transformation and finally T-dualize back to the original space. The transformation maps between string solutions with different boundary contours. The boundary contours of the minimal surfaces are not mapped back to the AdS boundary, and the regularized area of the surface changes.
We discuss chiral zero-rest-mass field equations on six-dimensional space-time from a twistorial point of view. Specifically, we present a detailed cohomological analysis, develop both Penrose and Penrose-Ward transforms, and analyse the corresponding contour integral formulae. We also give twistor space action principles. We then dimensionally reduce the twistor space of six-dimensional space-time to obtain twistor formulations of various theories in lower dimensions. Besides well-known twistor spaces, we also find a novel twistor space amongst these reductions, which turns out to be suitable…
We find general deformations of BTZ spacetime and identify the corresponding thermofield initial states of the dual CFT. We deform the geometry by introducing bulk fields dual to primary operators and find the back-reacted gravity solutions to the quadratic order of the deformation parameter. The dual thermofield initial states can be deformed by inserting arbitrary linear combination of operators at the mid-point of the Euclidean time evolution that appears in the construction of the thermofield initial states. The deformed geometries are dual to thermofield states without deforming the bound…
We construct a new supertwistor space suited for establishing a Penrose-Ward transform between certain bundles over this space and solutions to the N=8 super Yang-Mills equations in three dimensions. This mini-superambitwistor space is obtained by dimensional reduction of the superambitwistor space, the standard superextension of the ambitwistor space. We discuss in detail the construction of this space and its geometry before presenting the Penrose-Ward transform. We also comment on a further such transform for purely bosonic Yang-Mills-Higgs theory in three dimensions by considering third or…
The Hawking-Penrose theorem is not covariant under field redefinitions. Should the invariance under such transformations be a true principle in Nature, spacetime singularities become dubious objects. We here review the concept of covariant singularities, that is, singularities that are invariant under both spacetime diffeomorphisms and field redefinitions.
Motivated by the recent discussions of the Penrose limit of AdS_5\times S^5, we examine a more general class of supersymmetric pp-wave solutions of the type IIB theory, with a larger number of non-vanishing structures in the self-dual 5-form. One of the pp-wave solutions can be obtained as a Penrose limit of a D3/D3 intersection. In addition to 16 standard supersymmetries these backgrounds always allow for supernumerary supersymmetries. The latter are in one-to-one correspondence with the linearly-realised world-sheet supersymmetries of the corresponding exactly-solvable type IIB string action…
We use the Chern-Simons formulation of higher spin theories in three dimensions to study aspects of holographic W-gravity. Concepts which were useful in studies of pure bulk gravity theories, such as the Fefferman-Graham gauge and the residual gauge transformations, which induce Weyl transformations in the boundary theory and their higher spin generalizations, are reformulated in the Chern-Simons language. Flat connections that correspond to conformal and lightcone gauges in the boundary theory are considered.
Using the relation between diffeomorphisms in the bulk and Weyl transformations on the boundary we study the Weyl transformation properties of the bulk metric on shell and of the boundary action. We obtain a universal formula for one of the classes of trace anomalies in any even dimension in terms of the parameters of the gravity action.
We consider the generalization of the S-duality transformation previously investigated in the context of the FQHE and s-wave superconductivity to p-wave superconductivity in 2+1 dimensions in the framework of the AdS/CFT correspondence. The vector Cooper condensate transforms under the S-duality action to the pseudovector condensate at the dual side. The 3+1-dimensional Einstein-Yang-Mills theory, the holographic dual to p-wave superconductivity, is used to investigate the S-duality action via the AdS/CFT correspondence. It is shown that in order to implement the duality transformation, chemic…
We reformulate Euclidean general relativity without cosmological constant as an action governing the complex structure of twistor space. Extending Penrose's non-linear graviton construction, we find a correspondence between twistor spaces with partially integrable almost complex structures and four-dimensional space-times with off-shell metrics. Using this, we prove that our twistor action reduces to Plebanski's action for general relativity via the Penrose transform. This should lead to new insights into the geometry of graviton scattering as well as to the derivation of computational tools l…
We extend the holographic duality between 3d pure gravity and the 2d Ising CFT proposed in [Phys. Rev. D 85 (2012) 024032] to CFTs with boundaries. Besides the usual asymptotic boundary, the dual bulk spacetime now has a real cutoff, on which live branes with finite tension, giving Neumann boundary condition on the metric tensor. The strongly coupled bulk theory requires that we dress the well-known semiclassical AdS/BCFT answer with boundary gravitons, turning the partition function into the form of Virasoro characters. Using this duality, we relate the brane tensions to the modular S-matrix …
Near-superradiant scattering of charged scalars and fermions by a near-extreme Kerr-Newman black hole and photons and gravitons by a near-extreme Kerr black hole are computed as certain Fourier transforms of correlators in a two-dimensional conformal field theory. The results agree with the classic spacetime calculations from the 1970s, thereby providing good evidence for a conjectured Kerr-Newman/CFT correspondence.
We construct a supersymmetric generalization of the holographic dual of a fractional topological insulator found in \cite{HoyosBadajoz:2010ac}. This is accomplished by introducing a nontrivial gauge field on the world volume of the probe D7 brane. The BPS equations are derived from the $κ$-symmetry transformation of the probe brane. The BPS equations are shown to reduce to two first oder nonlinear partial differential equations. Solutions of the BPS equations correspond to a probe brane configuration which preserves four of the thirty-two supersymmetries of the $AdS_5\times S^5$ background. So…
A quantum-field theoretical interpretation is given to the holographic RG equation by relating it to a field-theoretical local RG equation which determines how Weyl invariance is broken in a quantized field theory. Using this approach we determine the relation between the holographic C theorem and the C theorem in two-dimensional quantum field theory which relies on the Zamolodchikov metric. Similarly we discuss how in four dimensions the holographic C function is related to a conjectured field-theoretical C function. The scheme dependence of the holographic RG due to the possible presence of …
Positive energy unitary irreducible representations of $SU(2,2)$ can be constructed with the aid of bosonic oscillators in (anti)fundamental representation of $SU(2)_L\times SU(2)_R$ that are closely related to Penrose twistors. Starting with the correspondence between the doubleton representations, homogeneous functions on projective twistor space and on-shell $SL(2,\mathbb C)$ generalized Weyl curvature spinors and their low-spin counterparts, we study in the similar way the correspondence between the massless representations, homogeneous functions on ambitwistor space and, via the Penrose t…
Applying recursive renormalization group transformations to a scalar field theory, we obtain an effective quantum gravity theory with an emergent extra dimension, described by a dual holographic Einstein-Klein-Gordon type action. Here, the dynamics of both the dual order-parameter field and the metric tensor field originate from density-density and energy-momentum tensor-tensor effective interactions, respectively, in the recursive renormalization group transformation, performed approximately in the Gaussian level. This linear approximation in the recursive renormalization group transformation…
We find new type II backgrounds with non-relativistic symmetries via non-Abelian T-duality. First we consider geometries with Galilean symmetries in type IIA, which have been identified as non-relativistic generalizations of the ABJM background and massive IIA supergravities. We then consider the non-Abelian T-duality transformation on the backgrounds with Lifshitz symmetry constructed by Donos and Gauntlett. Using gauge/gravity duality we study aspects of the field theory dual to these backgrounds.
In this paper we study the application of holographic entanglement negativity proposal for bipartite states in the 2d Galilean conformal field theory ($GCFT_2$) dual to bulk asymptotically flat spacetimes in the context of generalized minimal massive gravity (GMMG) model. $GCFT_2$ is considered on the boundary side of the duality and the bulk gravity is described by GMMG that is asymptotically symmetric under the Galilean conformal transformations. In this paper, the replica technique, based on the two-point and the four-point twist correlators, is utilized and the entanglement entropy and the…
We show that the string worldsheet theory of Gaiotto-Maldacena holographic duals to N=2 superconformal field theories generically fails to be classically integrable. We demonstrate numerically that the dynamics of a winding string configuration possesses a non-vanishing Lyapunov exponent. Furthermore an analytic study of the Normal Variational Equation fails to yield a Liouvillian solution. An exception to the generic non-integrability of such backgrounds is provided by the non-Abelian T-dual of $AdS_5 \times S^5$. Here by virtue of the canonical transformation nature of the T-duality classica…
We consider higher-spin gravity in (Euclidean) AdS_4, dual to a free vector model on the 3d boundary. In the bulk theory, we study the linearized version of the Didenko-Vasiliev black hole solution: a particle that couples to the gauge fields of all spins through a BPS-like pattern of charges. We study the interaction between two such particles at leading order. The sum over spins cancels the UV divergences that occur when the two particles are brought close together, for (almost) any value of the relative velocity. This is a higher-spin enhancement of supergravity's famous feature, the cancel…
Hughston has shown that projective pure spinors can be used to construct massless solutions in higher dimensions, generalizing the four-dimensional twistor transform of Penrose. In any even (Euclidean) dimension d=2n, projective pure spinors parameterize the coset space SO(2n)/U(n), which is the space of all complex structures on R^{2n}. For d=4 and d=6, these spaces are CP^1 and CP^3, and the appropriate twistor transforms can easily be constructed. In this paper, we show how to construct the twistor transform for d>6 when the pure spinor satisfies nonlinear constraints, and present explicit …
The Multiscale Entanglement Renormalization Ansatz (MERA) is a tensor network based variational ansatz that is capable of capturing many of the key physical properties of strongly correlated ground states such as criticality and topological order. MERA also shares many deep relationships with the AdS/CFT (gauge-gravity) correspondence by realizing a UV complete holographic duality within the tensor networks framework. Motivated by this, we have re-purposed the MERA tensor network as an analysis tool to study the real-time evolution of the 1D transverse Ising model in its low energy excited sta…
We present the main ingredients of twistor theory leading up to and including the Penrose-Ward transform in a coordinate algebra form which we can then `quantise' by means of a functorial cocycle twist. The quantum algebras for the conformal group, twistor space CP^3, compactified Minkowski space CMh and the twistor correspondence space are obtained along with their canonical quantum differential calculi, both in a local form and in a global *-algebra formulation which even in the classical commutative case provides a useful alternative to the formulation in terms of projective varieties. We o…
We derive an effective dual holographic Einstein-Maxwell theory, applying renormalization group transformations to interacting Dirac fermions in a recursive way. In particular, we show how both background metric tensor and U(1) gauge fields become dynamical to describe the renormalization group flows of coupling functions and order parameter fields of the corresponding quantum field theory through natural emergence of an extra-dimensional space, respectively. Finally, we propose a prescription on how to calculate correlation functions in a non-perturbative way, where quantum fluctuations of bo…
We compute the holographic entanglement entropy in the gravity with higher curvature terms dual to d=4 N=2 SCFTs in F-theory using the method proposed in arXiv:1011.5819. The log term of this entanglement entropy reproduces the A-type anomaly of the dual SCFTs in F- theory using the gravity dual with the higher derivative term, which, using the field redefinition, can be transformed to the Gauss-Bonnet term in the subleading order of a derivative expansion. Our analysis shows that the 1/N^2 correction for the central charges should be produced from the gravity including higher derivative terms…
To clarify the mathematical structure of the RG-derived holographic dual field theory, we rewrite the string-theory based conventionally utilized dual holographic effective field theory based on the ADM decomposition of the metric tensor. This comparison leads us to claim that the RG-derived emergent holographic dual field theory takes into account higher-derivative curvature terms with gauge fixing in the string-theory based conventionally utilized Einstein-Klein-Gordon theory, giving rise to the RG flow of the metric tensor beyond the AdS (anti-de Sitter space) geometry. Furthermore, we comp…
We elaborate on our earlier proposal connecting entanglement renormalization and holographic duality in which we argued that a tensor network can be reinterpreted as a kind of skeleton for an emergent holographic space. Here we address the question of the large $N$ limit where on the holographic side the gravity theory becomes classical and a non-fluctuating smooth spacetime description emerges. We show how a number of features of holographic duality in the large $N$ limit emerge naturally from entanglement renormalization, including a classical spacetime generated by entanglement, a sparse sp…
