Penrose Limit Research Articles

Generalized complex marginal deformation of pp-waves and giant gravitons

We present the Penrose limits of a complex marginal deformation of AdS5×S5, which incorporates the SL(2,R) symmetry of type IIB theory, along the (J,0,0) geodesic and along the (J,J,J) geodesic. We discuss giant gravitons on the deformed (J,0,0) pp-wave background.

Spherical collapse of small masses in the ghost-free gravity

We discuss some properties of recently proposed models of a ghost-free gravity. For this purpose we study solutions of linearized gravitational equations in the framework of such a theory. We mainly focus on the version of the ghost-free theory with the exponential modification exp(□/μ 2)□−1 of the free propagator. The following three problems are discussed: (i) gravitational field of a point mass; (ii) Penrose limit of a point source boosted to the speed of light; and (iii) spherical gravitational collapse of null fluid. For the first problem we demonstrate that it can be solved by using the method of heat kernels and obtain a solution in a spacetime with arbitrary number of dimensions. For the second problem we also find the corresponding gyraton-type solutions of the ghost-free gravitational equations for any number of dimensions. For the third problem we obtain solutions for the gravitational field for the collapse of both “thin” and “thick” spherical null shells. We demonstrate how the ghost-free modification of the gravitational equations regularize the solutions of the linearized Einstein equations and smooth out their singularities.

Semiclassical strings in supergravity PFT

Puff field theory (PFT) is an example of a non-local field theory which arises from a novel embedding of D-branes in a Melvin universe. We study several rotating and pulsating string solutions of the F-string equations of motion in the supergravity dual of the PFT. Further, we find a PP-wave geometry from this non-local spacetime by applying a Penrose limit and comment on its similarity with the maximally supersymmetric PP-wave background.

Semiclassical strings and non-Abelian T-duality

We study semiclassical strings in the Klebanov–Witten and in the non-Abelian T-dual Klebanov–Witten backgrounds. We show that both backgrounds share a subsector of equivalent states up to conditions on the T-dual coordinates. We also analyse string configurations where the strings are stretched along the T-dual coordinates. This semiclassical analysis predicts the existence of (almost) chiral primary operators for the dual superconformal field theory whose (anomalous) bare dimensions depend on the T-dual coordinates. We briefly discuss the Penrose limit of the dualised background.

β-deformation on a slanted torus and deformedppwave

We discuss the $\ensuremath{\beta}$-deformation of ${\mathrm{AdS}}_{5}\ifmmode\times\else\texttimes\fi{}{S}^{5}$ which incorporates the $SL(2,\mathbb{R})$ symmetry of the type IIB theory. The axion-dilaton is identified with a two-torus from an 11-dimensional viewpoint. We consider the null geodesic with equal component angular momenta to take the Penrose limit of the deformed ${\mathrm{AdS}}_{5}\ifmmode\times\else\texttimes\fi{}{S}^{5}$. We study the bosonic part of the string sigma model and the spectrum of the string in the $pp$-wave background.

Tidal stretching of gravitons into classical strings: application to jet quenching with AdS/CFT

Previous work has shown that the standard supergravity approximation can break down when using AdS/CFT duality to study certain top-down formulations of the jet stopping problem in strongly-coupled N=4 super-Yang-Mills (SYM) plasmas, depending on the virtuality of the source of the "jet." In this paper, we identify the nature of this breakdown: High-momentum gravitons in the gravitational dual get stretched into relatively large classical string loops by tidal forces associated with the black brane. These stringy excitations of the graviton are not contained in the supergravity approximation, but we show that the jet stopping problem can nonetheless still be solved by drawing on various string-theory methods (the eikonal approximation, the Penrose limit, string quantization in pp-wave backgrounds) to obtain a probability distribution for the late-time classical string loops. In extreme cases, we find that the gravitons are stretched into very long folded strings which are qualitatively similar to the folded classical strings originally used by Gubser, Gulotta, Pufu and Rocha to model the jet stopping problem. This makes a connection in certain cases between the different methods that have been used to study jet stopping with AdS/CFT and gives a specific example of a precise N=4 SYM problem that generates such strings in the gravity description.

THE UNBEARABLE BEINGNESS OF LIGHT — Dressingand Undressing Photonsin Black Hole Spacetimes

Gravitational tidal forces acting on the virtual e+e- cloud surrounding a photon endow spacetime with a nontrivial refractive index. This has remarkable properties unique to gravitational theories including superluminal low-frequency propagation, in apparent violation of causality, and amplification of the renormalized photon field, in apparent violation of unitarity. Using the geometry of null congruences and the Penrose limit, we illustrate these phenomena and their resolution by tracing the history of a photon as it falls into the near-singularity region of a black hole.

Three-point functions of BMN operators at weak and strong coupling II. One loop matching

In a previous paper, arXiv:1204.3096, we have shown that the fully dynamical three-point correlation functions of BMN operators are identical at the tree level in the planar limit of perturbative field theory and, on the string theory side, calculated by means of the Dobashi-Yoneya three string vertex in the Penrose limit. Here we present a one-loop calculation of the same quantity both on the field-theory and string-theory side, where a complete identity between the two results is demonstrated.

Flat limit of three dimensional asymptotically anti–de Sitter spacetimes

In order to get a better understanding of holographic properties of gravitational theories with a vanishing cosmological constant, we analyze in detail the relation between asymptotically anti-de Sitter and asymptotically flat spacetimes in three dimensions. This relation is somewhat subtle because the limit of vanishing cosmological constant cannot be naively taken in standard Fefferman-Graham coordinates. After reformulating the standard anti-de Sitter results in Robinson-Trautman coordinates, a suitably modified Penrose limit is shown to connect both asymptotic regimes.

Caustics and wave propagation in curved spacetimes

We investigate the effects of light cone caustics on the propagation of linear scalar fields in generic four-dimensional spacetimes. In particular, we analyze the singular structure of relevant Green functions. As expected from general theorems, Green functions associated with wave equations are globally singular along a large class of null geodesics. Despite this, the "nature" of the singularity on a given geodesic does not necessarily remain fixed. It can change character on encountering caustics of the light cone. These changes are studied by first deriving global Green functions for scalar fields propagating on smooth plane wave spacetimes. We then use Penrose limits to argue that there is a sense in which the "leading order singular behavior" of a (typically unknown) Green function associated with a generic spacetime can always be understood using a (known) Green function associated with an appropriate plane wave spacetime. This correspondence is used to derive a simple rule describing how Green functions change their singular structure near some reference null geodesic. Such changes depend only on the multiplicities of the conjugate points encountered along the reference geodesic. Using sigma(p,p') to denote a suitable generalization of Synge's world function, conjugate points with multiplicity 1 convert Green function singularities involving delta(sigma) into singularities involving 1/pi sigma (and vice-versa). Conjugate points with multiplicity 2 may be viewed as having the effect of two successive passes through conjugate points with multiplicity 1.

Power indices in large voting bodies

There is no consensus on the properties of voting power indices when there is a large number of voters in a weighted-voting body. On the one hand, in some real-world cases that have been studied the power indices have been found to be nearly proportional to the weights (e.g., the EUCM, US Electoral College); this is true for both the Penrose-Banzhaf and the Shapley-Shubik indices. It has been suggested that this is a manifestation of a conjecture by Penrose (known subsequently as the Penrose limit theorem, that has been shown to hold under certain conditions). On the other hand, we have the older literature from cooperative game theory, due to Shapley and his collaborators, showing that, where there is a finite number of voters whose weights remain constant in relative terms, and where the quota remains constant in relative terms, while the total number of voters increases without limit, the powers of the voters with finite weight tend to limiting values that are, in general, not proportional to the weights. These results, too, are supported by empirical studies of large voting bodies (e.g., the IMF/WB boards, corporate shareholder meetings). This paper proposes a restatement of the Penrose limit theorem and shows that, in general, both the ‘classical’ power indices converge in the limit to proportionality with weights as the Laakso-Taagepera index of political fragmentation increases. This new version reconciles the different theoretical and empirical results that have been found for large voting bodies.

Note on I-brane near horizon PP-wave background

We find out a PP-wave spacetime with constant Neveu–Schwarz (NS) three form flux by taking a Penrose limit on the ( 1 + 1 ) -dimensional intersection of two orthogonal stacks of fivebranes in type IIB string theory. We further find out an intersecting (D1–D5)-brane solution in this background and analyze its supersymmetry properties by solving the dilatino and gravitino variations explicitly.

Any spacetime has a Bianchi type I spacetime as a limit

Pick an arbitrary timelike geodesic in an arbitrary spacetime. We shall demonstrate that there is a particular limiting process, an ‘ultra-local limit’, in which the immediate tube-like neighbourhood of the timelike geodesic can be ‘blown up’ to yield a general (typically non-diagonal) Bianchi-type I spacetime. This process shares some (but definitely not all) of the features of the Penrose limit, whereby the immediate tube-like neighbourhood of an arbitrary null geodesic is ‘blown up’ to yield a pp-wave as a limit.

Correspondence between Asymptotically Flat Spacetimes and Nonrelativistic Conformal Field Theories

We find a surprising connection between asymptotically flat spacetimes and nonrelativistic conformal systems in one lower dimension. The Bondi-Metzner-Sachs (BMS) group is the group of asymptotic isometries of flat Minkowski space at null infinity. This is known to be infinite dimensional in three and four dimensions. We show that the BMS algebra in 3 dimensions is the same as the 2D Galilean conformal algebra (GCA) which is of relevance to nonrelativistic conformal symmetries. We further justify our proposal by looking at a Penrose limit on a radially infalling null ray inspired by nonrelativistic scaling and obtain a flat metric. The BMS4 algebra is also discussed and found to be the same as another class of GCA, called semi-GCA, in three dimensions. We propose a general BMS-GCA correspondence. Some consequences are discussed.

SU(2|2)for theories with sixteen supercharges at weak and strong coupling

We consider the dimensional reductions of N=4 Supersymmetric Yang-Mills theory on R x S^3 to the three-dimensional theory on R x S^2, the orbifolded theory on R x S^3/Z_k, and the plane-wave matrix model. With explicit emphasis on the three-dimensional theory, we demonstrate the realization of the SU(2|3) algebra in a radial Hamiltonian framework. Using this structure we constrain the form of the spin chains, their S-matrices, and the corresponding one- and two-loop Hamiltonian of the three dimensional theory and find putative signs of integrability up to the two-loop order. The string duals of these theories admit the IIA plane-wave geometry as their Penrose limit. Using known results for strings quantized on this background, we explicitly construct the strong-coupling dual extended SU(2|2) algebra and discuss its implications for the gauge theories.

New Penrose limits and AdS/CFT

We find a new Penrose limit of AdS_5 x S^5 giving the maximally supersymmetric pp-wave background with two explicit space-like isometries. This is an important missing piece in studying the AdS/CFT correspondence in certain subsectors. In particular whereas the Penrose limit giving one space-like isometry is useful for the SU(2) sector of N=4 SYM, this new Penrose limit is instead useful for studying the SU(2|3) and SU(1,2|3) sectors. In addition to the new Penrose limit of AdS_5 x S^5 we also find a new Penrose limit of AdS_4 x CP^3.

The refractive index of curved spacetime II: QED, Penrose limits and black holes

This work considers the way that quantum loop effects modify the propagation of light in curved space. The calculation of the refractive index for scalar QED is reviewed and then extended for the first time to QED with spinor particles in the loop. It is shown how, in both cases, the low frequency phase velocity can be greater than c, as found originally by Drummond and Hathrell, but causality is respected in the sense that retarded Green functions vanish outside the lightcone. A ``phenomenology'' of the refractive index is then presented for black holes, FRW universes and gravitational waves. In some cases, some of the polarization states propagate with a refractive index having a negative imaginary part indicating a potential breakdown of the optical theorem in curved space and possible instabilities.

Spin chains in 𝒩 = 6 superconformal Chern-Simons-Matter theory

In this note we study spin chain operators in the = 6 Chern-Simons-matter theory recently proposed by Aharony, Bergman, Jafferis and Maldacena to be dual to type IIA string theory in AdS4 × 3. We study the two-loop dilatation operator in the gauge theory, and compare to the Penrose limit on the string theory side.

The causal structure of QED in curved spacetime: analyticity and the refractive index

The effect of vacuum polarization on the propagation of photons in curved spacetime is studied in scalar QED. A compact formula is given for the full frequency dependence of the refractive index for any background in terms of the Van Vleck-Morette matrix for its Penrose limit and it is shown how the superluminal propagation found in the low-energy effective action is reconciled with causality. The geometry of null geodesic congruences is found to imply a novel analytic structure for the refractive index and Green functions of QED in curved spacetime, which preserves their causal nature but violates familiar axioms of S-matrix theory and dispersion relations. The general formalism is illustrated in a number of examples, in some of which it is found that the refractive index develops a negative imaginary part, implying an amplification of photons as an electromagnetic wave propagates through curved spacetime.

Finite-size corrections in the [formula omitted] sector of type IIA string theory on [formula omitted

We consider finite-size corrections in the SU ( 2 ) × SU ( 2 ) sector of type IIA string theory on AdS 4 × C P 3 , which is the string dual of the recently constructed N = 6 superconformal Chern–Simons theory of Aharony, Bergman, Jafferis and Maldacena (ABJM theory). The string states we consider are in the R × S 2 × S 2 subspace of AdS 4 × C P 3 with an angular momentum J on C P 3 being large. We compute the finite-size corrections using two different methods, one is to consider curvature corrections to the Penrose limit giving an expansion in 1 / J , the other by considering a low energy expansion in λ ′ = λ / J 2 of the string theory sigma-model, λ being the 't Hooft coupling of the dual ABJM theory. For both methods there are interesting issues to deal with. In the near-pp-wave method there is a 1 / J interaction term for which we use zeta-function regularization in order to compute the 1 / J correction to the energy. For the low energy sigma-model expansion we have to take into account a non-trivial coupling to a non-dynamical transverse direction. We find agreement between the two methods. At order λ ′ and λ ′ 2 , for small λ ′ , our results are analogous to the ones for the SU ( 2 ) sector in type IIB string theory on AdS 5 × S 5 . Instead at order λ ′ 3 there are interactions between the two two-spheres. We compare our results with the recently proposed all-loop Bethe ansatz of Gromov and Vieira and find agreement.