We show that the conformal Penrose limit is an ordinary plane wave limit in a higher dimensional framework which resolves the spacetime singularity. The higher dimensional framework is provided by Ricci-flat manifolds which are of the form M_D = M_d x B, where M_d is an Einstein spacetime that has a negative cosmological constant and admits a spacelike conformal Killing vector, and B is a complete Sasaki-Einstein space with constant sectional curvature. We define the Kaluza-Klein metric of M_D through the conformal Killing potential of M_d and prove that M_d has a conformal Penrose limit if and only if M_D has an ordinary plane wave limit. Further properties of the limit are discussed.
A generalization of the limiting procedure of Penrose, which allows non-zero cosmological constants and takes into account metrics that contain homogeneous functions of degree zero, is presented. It is shown that any spacetime which admits a spacelike conformal Killing vector has a limit which is conformal to plane waves. If the spacetime is an Einstein space, its limit exists only if the cosmological constant is negative or zero. When the conformal Killing vector is hypersurface orthogonal, the limits of Einstein spacetimes are certain AdS plane waves. In this case the nonlinear version of th…
The symmetry algebra of asymptotically flat spacetimes at null infinity in four dimensions in the sense of Newman and Unti is revisited. As in the Bondi-Metzner-Sachs gauge, it is shown to be isomorphic to the direct sum of the abelian algebra of infinitesimal conformal rescalings with bms4. The latter algebra is the semi-direct sum of infinitesimal supertranslations with the conformal Killing vectors of the Riemann sphere. Infinitesimal local conformal transformations can then consistently be included. We work out the local conformal properties of the relevant Newman-Penrose coefficients, con…
Projecting on a suitable subset of coordinates, a picture is constructed in which the conformal boundary of $AdS_5\times S^5$ and that of the plane wave resulting in the Penrose limit are located at the same line. In a second line of arguments all $AdS_5\times S^5$ and plane wave geodesics are constructed in their integrated form. Performing the Penrose limit, the approach of null geodesics reaching the conformal boundary of $AdS_5\times S^5$ to that of the plane wave is studied in detail. At each point these null geodesics of $AdS_5\times S^5$ form a cone which degenerates in the limit.
In this paper we study the Penrose limit of AdS_5 orbifolds. The orbifold can be either in the pure spatial directions or space and time directions. For the AdS_5/Γ\times S^5 spatial orbifold we observe that after the Penrose limit we obtain the same result as the Penrose limit of AdS_5\times S^5/Γ. We identify the corresponding BMN operators in terms of operators of the gauge theory on R\times S^3/Γ. The semi-classical description of rotating strings in these backgrounds have also been studied. For the spatial AdS orbifold we show that in the quadratic order the obtained action for the fluctu…
We consider the exact solutions of the supergravity theories in various dimensions in which the space-time has the form M_{d} x S^{D-d} where M_{d} is an Einstein space admitting a conformal Killing vector and S^{D-d} is a sphere of an appropriate dimension. We show that, if the cosmological constant of M_{d} is negative and the conformal Killing vector is space-like, then such solutions will have a conformal Penrose limit: M^{(0)}_{d} x S^{D-d} where M^{(0)}_{d} is a generalized d-dimensional AdS plane wave. We study the properties of the limiting solutions and find that M^{(0)}_{d} has 1/4 s…
We investigate the Penrose limits of classical string and M-theory backgrounds. We prove that the number of (super)symmetries of a supergravity background never decreases in the limit. We classify all the possible Penrose limits of AdS x S spacetimes and of supergravity brane solutions. We also present the Penrose limits of various other solutions: intersecting branes, supersymmetric black holes and strings in diverse dimensions, and cosmological models. We explore the Penrose limit of an isometrically embedded spacetime and find a generalisation to spaces with more than one time. Finally, we …
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 show how the Szekeres form of the line element is naturally adapted to study Penrose limits in classical string backgrounds. Relating the "old" colliding wave problem to the Penrose limiting procedure as employed in string theory we discuss how two orthogonal Penrose limits uniquely determine the underlying target space when certain symmetry is imposed. We construct a conformally deformed background with two distinct, yet exactly solvable in terms of the string theory on R-R backgrounds, Penrose limits. Exploiting further the similarities between the two problems we find that the Penrose li…
We show that the causal properties of asymptotically flat spacetimes depend on their dimensionality: while the time-like future of any point in the past conformal infinity $\mathcal{I}^-$ contains the whole of the future conformal infinity $\mathcal{I}^+$ in $(2+1)$ and $(3+1)$ dimensional Schwarzschild spacetimes, this property (which we call the Penrose property) does not hold for $(d+1)$ dimensional Schwarzschild if $d>3$. We also show that the Penrose property holds for the Kerr solution in $(3+1)$ dimensions, and discuss the connection with scattering theory in the presence of positive ma…
We analyse the relation between two a priori quite different expansions of the string equations of motion and constraints in a general curved background, namely one based on the covariant Penrose-Fermi expansion of the metric G_{μν} around a Penrose limit plane wave associated to a null geodesic γ, and the other on the Riemann coordinate expansion in the exact metric G_{μν} of the string embedding variables around the null geodesic γ. Starting with the observation that there is a formal analogy between the exact string equations in a plane wave and the first order string equations in a general…
We study the conformal structure of exotic (non-big-bang) singularity universes using the hybrid big-bang/exotic singularity/big-bang and big-rip/exotic singularity/big-rip models by investigating their appropriate Penrose diagrams. We show that the diagrams have the standard structure for the big-bang and big-rip and that exotic singularities appear just as the constant time hypersurfaces for the time of a singularity and because of their geodesic completeness are potentially transversable. We also comment on some applications and extensions of the Penrose diagram method in studying exotic si…
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.
We consider M-theory on AdS_4 x V_{5,2} where V_{5,2}= SO(5)/SO(3) is a Stiefel manifold. We construct a Penrose limit of AdS_4 x V_{5,2} that provides the pp-wave geometry. There exists a subsector of three dimensional N=2 dual gauge theory, by taking both the conformal dimension and R charge large with the finiteness of their difference, which has enhanced N=8 maximal supersymmetry. We identify operators in the N=2 gauge theory with supergravity KK excitations in the pp-wave geometry and describe how the gauge theory operators made out of chiral field of conformal dimension 1/3 fall into N=8…
We show that the maximally supersymmetric pp-waves of IIB superstring and M-theories can be obtained as a Penrose limit of the supersymmetric AdS x S solutions. In addition we find that in a certain large tension limit, the geometry seen by a brane probe in an AdS x S background is either Minkowski space or a maximally supersymmetric pp-wave.
In this paper we consider both Abelian as well as non-Abelian T-duals of the Klebanov-Witten background and inspect their various Penrose limits. We show that these backgrounds admit pp-wave solutions in the neighbourhood of appropriate null geodesics. We study the quantization of closed string propagating on some of the resulting pp-wave backgrounds and comment on the probable field theory duals.
In this paper we consider the Klebanov-Tseytlin background and its non-Abelian T-dual geometry along a suitably chosen $SU(2)$ subgroup of isometries. We analyse the Penrose limits along various null geodesics of both the geometries. We observe that, the Klebanov-Tseytlin geometry does not admit any pp-wave solutions. However, the T-dual background gives rise to pp-wave solution upon taking the Penrose limit along some appropriate null geodesic. We comment on the possible gauge theory dual for our pp-wave background.
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 investigate the Penrose limit of various brane solutions including Dp-branes, NS5-branes, fundamental strings, (p,q) fivebranes and (p,q) strings. We obtain special null geodesics with the fixed radial coordinate (critical radius), along which the Penrose limit gives string theories with constant mass. We also study string theories with time-dependent mass, which arise from the Penrose limit of the brane backgrounds. We examine equations of motion of the strings in the asymptotic flat region and around the critical radius. In particular, for (p,q) fivebranes, we find that the string equatio…
We construct plane wave backgrounds with time-dependent profiles corresponding to Penrose limits of NS5-branes with transverse space symmetry group broken from SO(4) to SO(2)\times Z_N. We identify the corresponding exact theory as the five-dimensional Logarithmic Conformal Field Theory (CFT) arising from the contraction of the SU(2)_{N'}/U(1)\times SL(2,R)_{-N} exact CFT, times R^5. We study several general aspects and construct the free field representation in this theory. String propagation and spectra are also considered and explicitly solved in the light-cone gauge.
Spin Matrix theory (SMT) limits provide a way to capture the dynamics of the AdS/CFT correspondence near BPS bounds. On the string theory side, these limits result in non-relativistic sigma models that can be interpreted as novel non-relativistic strings. This SMT string theory couples to non-relativistic $U(1)$-Galilean background geometries. In this paper, we explore the relation between pp-wave backgrounds obtained from Penrose limits of AdS${}_5 \times S^5$, and a new type of $U(1)$-Galilean backgrounds that we call flat-fluxed (FF) backgrounds. These FF backgrounds are the simplest possib…
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 construct a Penrose limit of AdS_4 x M^{1,1,1} where M^{1,1,1}= SU(3) x SU(2) x U(1)/(SU(2) x U(1) x U(1)) that provides the pp-wave geometry equal to the one in the Penrose limit of AdS_4 x S^7. There exists a subsector of three dimensional N=2 dual gauge theory which has enhanced N=8 maximal supersymmetry. We identify operators in the N=2 gauge theory with supergravity KK excitations in the pp-wave geometry and describe how the gauge theory operators made out of two kinds of chiral fields of conformal dimension 4/9, 1/3 fall into N=8 supermultiplets.
In this paper we consider the non-Abelian T-dual geometry of the type $IIB$ supergravity theory on $AdS_3\times S^3\times T^4$ background along a convenient $SU(2)$ subgroup of the $SO(4)$ R-symmetry. We examine various null geodesics of the resulting massive type $IIA$ supergravity theory and investigate the Penrose limits along these geodesics. We find that one of the resulting backgrounds admits pp-wave geometry in the neighbourhood of a suitable null geodesic. We carry out the supersymmetry analysis of the resulting pp-wave geometry and observe that it preserves sixteen supercharges. Furth…
We use Weyl transformations between the Minkowski spacetime and dS/AdS spacetime to show that one cannot well define the electrodynamics globally on the ordinary conformal compactification of the Minkowski spacetime (or dS/AdS spacetime), where the electromagnetic field has a sign factor (and thus is discountinuous) at the light cone. This problem is intuitively and clearly shown by the Penrose diagrams, from which one may find the remedy without too much difficulty. We use the Minkowski and dS spacetimes together to cover the compactified space, which in fact leads to the doubled conformal co…
Impulsive gravitational waves in Minkowski space were introduced by Roger Penrose at the end of the 1960s, and have been widely studied over the decades. Here we focus on nonexpanding waves which later have been generalized to impulses traveling in all constant-curvature backgrounds, i.e., the (anti-)de Sitter universe. While Penrose's original construction was based on his vivid geometric "scissors-and-paste" approach in a flat background, until recently a comparably powerful visualization and understanding has been missing in the case with a cosmological constant $Λ\not=0$. Here we review th…
We construct the Penrose limit backgrounds in closed forms along the generic null geodesics for the near-horizon geometries of D1, D3, D5, NS1 and NS5 branes. The Penrose limit metrics of D1, D5 and NS1 have non-trivial dependence of the light-cone time coordinate, while those of D3 and NS5 have no its dependence. We study the Penrose limits on the marginal 1/4 supersymmetric configurations of standard intersecting branes, such as the NS-NS intersection of NS1 and NS5, the R-R intersections of Dp and Dq over some spatial dimensions and the mix intersections of NS5 and Dp over (p -1)-dimensiona…
Departing from the observation that the Penrose limit of AdS_3 x S^3 is a group contraction in the sense of Inonu and Wigner, we explore the relation between the symmetric D-branes of AdS_3 x S^3 and those of its Penrose limit, a six-dimensional symmetric plane wave analogous to the four-dimensional Nappi--Witten spacetime. Both backgrounds are Lie groups admitting bi-invariant lorentzian metrics and symmetric D-branes wrap their (twisted) conjugacy classes. We determine the (twisted and untwisted) symmetric D-branes in the plane wave background and we prove the existence of a space-filling D5…
We consider a family of pp-wave solutions of IIB supergravity. This family has a non-trivial, constant 5-form flux, and non-trivial, (light-cone) time-dependent RR and NS-NS 3-form fluxes. The solutions have either 16 or 20 supersymmetries depending upon the time dependence. One member of this family of solutions is the Penrose limit of the solution obtained by Pilch and Warner as the dual of a Leigh-Strassler fixed point. The family of solutions also provides indirect evidence in support of a recent conjecture concerning a large N duality group that acts on RG flows of N=2 supersymmetric, qui…
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 discuss various Penrose limits of conformal and nonconformal backgrounds. In AdS_5 x T^{1,1}, for a particular choice of the angular coordinate in T^{1,1} the resulting Penrose limit coincides with the similar limit for AdS_5 x S^5. In this case an identification of a subset of field theory operators with the string zero modes creation operators is possible. For another limit we obtain a light-cone string action that resembles a particle in a magnetic field. We also consider three different types of backgrounds that are dual to nonconformal field theories: The Schwarzschild black hole in Ad…
We consider M-theory on AdS_4 x N^{0,1,0} where N^{0,1,0}= (SU(3) x SU(2))/(SU(2) x U(1)). We review a Penrose limit of AdS_4 x N^{0,1,0} that provides the pp-wave geometry of AdS_4 x S^7. There exists a subsector of three dimensional N=3 dual gauge theory, by taking both the conformal dimension and R-charge large with the finiteness of their difference, which has enhanced N=8 maximal supersymmetry. We identify operators in the N=3 gauge theory with supergravity KK excitations in the pp-wave geometry and describe how the N=2 gauge theory operators originating from both N=3 short vector multipl…
We consider open strings ending on a D5-brane in the pp-wave background, which is realized in the Penrose limit of $AdS_5 \times S^5$ with an $AdS_4\times S^2$ brane. A complete list of gauge invariant operators in the defect conformal field theory is constructed which is dual to the open string states.
We discuss the Green-Schwarz action for type IIB strings in general plane-wave backgrounds obtained as Penrose limits from any IIB supergravity solutions with vanishing background fermions. Using the normal-coordinate expansion in superspace, we prove that the light-cone action is necessarily quadratic in the fermionic coordinates. This proof is valid for more general pp-wave backgrounds under certain conditions. We also write down the complete quadratic action for general bosonic on-shell backgrounds in a form in which its geometrical meaning is manifest both in the Einstein and string frames…
Recently, Aharony, Bergman, Jafferis and Maldacena proposed that the N=6 Chern-Simons gauge theories are holographically dual to the M-theory backgrounds with multiple M2-branes on orbifolds C^4/Z_k. When k is large, they have the type IIA string description. In this paper we analyze the Penrose limit of this IIA background and express the string spectrum as the conformal dimensions of operators in the gauge theories. For BPS operators, we can confirm the agreements between the IIA string on plane waves and the gauge theories. We point out that there exist BMN-like operators in the gauge theor…
In this paper we construct generalised Penrose limits for the solutions of massive type IIA supergravity. We consider a Freund-Rubin type solution and apply these {\it massive} Penrose limits and obtain supersymmetric pp-wave which is a standard type IIA background. We point out that results in this paper are easily generalised for the cases of gauged supergravities.
We argue that the gauge theory dual to the Type IIB string theory in ten-dimensional pp-wave background can be thought to `live' on an {\it Euclidean} subspace spanning four of the eight transverse coordinates. We then show that light-cone time evolution of the string is identifiable as the RG flow of the gauge theory -- a relation facilitating `holography' of the pp-wave background. The `holography' reorganizes the dual gauge theory into theories defined over Hilbert subspaces of fixed R-charge. The reorganization breaks the SO(4,2)$\times$SO(6) symmetry to a maximal subgroup SO(4)$\times$ SO…
We analyse the causal structure of the two dimensional (2D) reduced background used in the perturbative treatment of a head-on collision of two $D$-dimensional Aichelburg-Sexl gravitational shock waves. After defining all causal boundaries, namely the future light-cone of the collision and the past light-cone of a future observer, we obtain characteristic coordinates using two independent methods. The first is a geometrical construction of the null rays which define the various light cones, using a parametric representation. The second is a transformation of the 2D reduced wave operator for th…
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…
We argue that the Penrose limit of a general string background is a generalization of the Seiberg-Sen limit describing M(atrix) theory as the DLCQ of M theory in flat space. The BMN theory of type IIB strings on the maximally supersymmetric pp-wave background is understood as the exact analogue of the BFSS M(atrix) theory, namely, a DLCQ of IIB string theory on $AdS_5 \times S^5$ in the limit of infinite longitudinal momentum. This point of view is used to explain some features of the BMN duality.
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.
We discuss a Penrose limit of an elliptic brane configuration with $N_1$ NS5 and $N_2$ D4 branes. This background is T-dual to $N_1$ D3 branes at a fixed point of a $\mathbf{C}^3/\mathbf{Z}_{N_2}$ singularity and the T-duality survives the Penrose limit. The triple scaling limit of $N_1$ and $N_2$ gives rise to IIA pp-wave solution with a space-like compact direction. We identify the quiver gauge theory operators and argue that upon exchange of the momentum along the compact direction and the winding number these operators coincide with the operators derived in the dual type IIB description. W…
We study the Penrose limit of the (p,q) fivebranes supergravity background. We consider the different phases of the worldvolume field theory and their weakly coupled descriptions. In the Penrose limit we get a solvable string theory and compute the spectrum. It corresponds to states of the six-dimensional worldvolume theory with large energy and large U(1) charge. We comment on the RG behavior of the gauge theory.
We extend the BMN duality between IIB superstring theory on a pp-wave background and a sector of N=4 super Yang-Mills theory to the non-supersymmetric and unstable background built by Romans as a compactification on a U(1) bundle over CP2 with 3-form and 5-form field strength fluxes. We obtain a stable theory with the fewest number of supercharges (e.g. 16) allowed by this kind of solutions and make conjectures on the dual gauge theory.
We consider the backgrounds obtained by Abelian and non-Abelian T-duality applied on $AdS_5\times S^5$. We study geodesics, calculate Penrose limits and find the associated plane-wave geometries. We quantise the weakly coupled type-IIA string theory on these backgrounds. We study the BMN sector, finding operators that wrap the original quiver CFT. For the non-Abelian plane wave, we find a 'flow' in the frequencies. We report some progress to understand this, in terms of deconstruction of a higher dimensional field theory. We explore a relation with the plane-wave limit of the Janus solution, w…
We study the Penrose limit of a supersymmetric IIB background, with non-trivial NS 3-form field strength, obtaining a solution with the smallest number of supercharges (i.e. 16) allowed; we write down explicitly the superalgebra of the theory, build the supersymmetric associated IIB string sigma model and make conjectures on the dual gauge theory.
Using Penrose diagrams the causal structure of the static spherically symmetric vacuum solution to conformal (Weyl) gravity is investigated. A striking aspect of the solution is an unexpected physical singularity at $r=0$ caused by a linear term in the metric. We explain how to calculate the deflection of light in coordinates where the metric is manifestly conformal to flat i.e. in coordinates where light moves in straight lines.
We describe the asymptotic boundary of the general homogeneous plane wave spacetime, using a construction of the `points at infinity' from the causal structure of the spacetime as introduced by Geroch, Kronheimer and Penrose. We show that this construction agrees with the conformal boundary obtained by Berenstein and Nastase for the maximally supersymmetric ten-dimensional plane wave. We see in detail how the possibility to go beyond (or around) infinity arises from the structure of light cones. We also discuss the extension of the construction to time-dependent plane wave solutions, focusing …
Kaigorodov spaces arise, after spherical compactification, as near horizon limits of M2, M5, and D3-branes with a particular pp-wave propagating in a world volume direction. We show that the uncompactified near horizon configurations K\times S are solutions of D=11 or D=10 IIB supergravity which correspond to perturbed versions of their AdS \times S analogues. We derive the Penrose-Gueven limits of the Kaigorodov space and the total spaces and analyse their symmetries. An Inonu-Wigner contraction of the Lie algebra is shown to occur, although there is a symmetry enhancement. We compare the res…
We generalize the classical junction conditions for constructing impulsive gravitational waves by the Penrose "cut and paste" method. Specifically, we study nonexpanding impulses which propagate in spaces of constant curvature with any value of the cosmological constant (that is Minkowski, de Sitter, or anti-de Sitter universes) when additional off-diagonal metric components are present. Such components encode a possible angular momentum of the ultra-relativistic source of the impulsive wave - the so called gyraton. We explicitly derive and analyze a specific transformation that relates the di…
We consider the Penrose limit of the solution of D5-brane given in the Anti-de Sitter space and analyse the shape of the D5-brane in the pp-wave background. We find that the D5-brane leads to the branes and the throats connecting the branes. The branes spread on R^4 with periodic values of the light-cone time x^+ and the throats lie along x^+. We also give some comments on holography.
A certain conformally invariant N=1 supersymmetric SU(n) gauge theory has a description as an infra-red fixed point obtained by deforming the N=4 supersymmetric Yang-Mills theory by giving a mass to one of its N=1 chiral multiplets. We study the Penrose limit of the supergravity dual of the large n limit of this N=1 gauge theory. The limit gives a pp-wave with R-R five-form flux and both R-R and NS-NS three-form flux. We discover that this new solution preserves twenty supercharges and that, in the light-cone gauge, string theory on this background is exactly solvable. Correspondingly, this la…
We obtain the Penrose limit of six dimensional Non-Commutative Open String (NCOS$_6$) theory and show that in the neighborhood of a particular null geodesic it leads to an exactly solvable string theory (unlike their counterparts in four or in other dimensions). We describe the phase structure of this theory and discuss the Penrose limit in different phases including Open D-string (OD1) theory. We compute the string spectrum and discuss their relations with the states of various theories at different phases. We also consider the case of general null geodesic for which the Penrose limit leads t…
The Penrose limits of a D5-brane wrapped on the sphere of AdS_5 x S^5 and connected to the boundary by M fundamental strings, which is dual to the baryon vertex of the N=4 SU(M) super Yang-Mills theory, are investigated. It is shown that, for null geodesics that lead to the maximally supersymmetric Hpp-wave background, the resulting D5-brane is a 1/2-supersymmetric null brane. For an appropriate choice of radial geodesic, however, the limiting configuration is 1/4-supersymmetric and closely related to the Penrose limit of a flat space BIon.
