Giant Graviton Solutions Research Articles

Giant gravitons on the Schr\xf6dinger pp-wave geometry

We construct a new giant graviton solution on the recently constructed pp-wave geometry of the non-supersymmetric Schrödinger background. That solution exhibits an intriguing behavior as the deformation parameter of the spacetime varies. Firstly, the degeneracy between the giant and the point graviton is lifted for the benefit of the giant graviton as soon as the deformation is turned on. Secondly, when the deformation parameter exceeds a critical value the barrier separating the point from the giant graviton disappears. This suggests that the mere presence of a D3-brane leads to the spontaneous breaking of conformal invariance. We perform a detailed analysis of the full bosonic spectrum, which reveals that the deformation induces a coupling between the scalar and the gauge field fluctuations. It is exactly this coupling that keeps the giant graviton free of tachyonic instabilities. Furthermore, the giant graviton configuration completely breaks the supersymmetry of the pp-wave background, as the Kappa-symmetry analysis suggests.

Null-wave giant gravitons from thermal spinning brane probes

We construct and analyze thermal spinning giant gravitons in type II/M-theory based on spherically wrapped black branes, using the method of thermal probe branes originating from the blackfold approach. These solutions generalize in different directions recent work in which the case of thermal (non-spinning) D3-brane giant gravitons was considered, and reveal a rich phase structure with various new properties. First of all, we extend the construction to M-theory, by constructing thermal giant graviton solutions using spherically wrapped M2- and M5-branes. More importantly, we switch on new quantum numbers, namely internal spins on the sphere, which are not present in the usual extremal limit for which the brane world volume stress tensor is Lorentz invariant. We examine the effect of this new type of excitation and in particular analyze the physical quantities in various regimes, including that of small temperatures as well as low/high spin. As a byproduct we find new stationary dipole-charged black hole solutions in AdS_m X S^n backgrounds of type II/M-theory. We finally show, via a double scaling extremal limit, that our spinning thermal giant graviton solutions lead to a novel null-wave zero-temperature giant graviton solution with a BPS spectrum, which does not have an analogue in terms of the conventional weakly coupled world volume theory.

From Schurs to giants in ABJ(M)

In this work we consider various correlators with Schur polynomials in ABJ(M) models that on the dual gravity side should correspond to processes involving giant gravitons. Our analysis imposes several constraints on the physics of the probe branes on AdS4xCP3 as well as sheds more light on giant graviton solutions in this background with additional NS B-field. Our main tool is a formula that we derive for extremal n-point functions of the single trace chiral primary operators in the free field theory limit. The formula expresses the correlators in terms of the two-point function of Schur polynomials labeled by hook diagrams and is valid for a large class of gauge theories. In particular, in N = 4 SYM, it proves the conjecture of Beisert et al.

Thermal Giant Gravitons

We study the giant graviton solution as the AdS_5 X S^5 background is heated up to finite temperature. The analysis employs the thermal brane probe technique based on the blackfold approach. We focus mainly on the thermal giant graviton corresponding to a thermal D3-brane probe wrapped on an S^3 moving on the S^5 of the background at finite temperature. We find several interesting new effects, including that the thermal giant graviton has a minimal possible value for the angular momentum and correspondingly also a minimal possible radius of the S^3. We compute the free energy of the thermal giant graviton in the low temperature regime, which potentially could be compared to that of a thermal state on the gauge theory side. Moreover, we analyze the space of solutions and stability of the thermal giant graviton and find that, in parallel with the extremal case, there are two available solutions for a given temperature and angular momentum, one stable and one unstable. In order to write down the equations of motion, action and conserved charges for the thermal giant graviton we present a slight generalization of the blackfold formalism for charged black branes. Finally, we also briefly consider the thermal giant graviton moving in the AdS_5 part.

Giant gravitons on deformed pp-waves

The recently constructed Lunin-Maldacena deformation of $AdS_{5}\times S^{5}$ is known to support two inequivalent Penrose limits that lead to BPS pp-wave geometries. In this note, we construct new giant graviton solutions on these backgrounds. A detailed study of the spectra of small fluctuations about these solutions reveals a remarkably rich structure. In particular, the giants that we contruct fall into two classes, one of which appears to remain stable in the Penrose limit independently of the strength of the deformation. The other class of giants, while more difficult to treat analytically, seems to exhibit a shape deformation not unlike the so-called "squashed giants" seen in the pp-wave with a constant NS $B$-field turned on. Some consideration is also given to the associated giant operators in the BMN limit of the dual ${\cal N}=1$ SYM gauge theory.

A KK-monopole giant graviton inAdS5×Y5

We construct a new giant graviton solution in AdS5 × Y5, with Y5 a quasi-regular Sasaki-Einstein manifold, consisting on a Kaluza-Klein monopole wrapped around the Y5 and with its Taub-NUT direction in AdS5. We find that this configuration has minimal energy when put in the centre of AdS5, where it behaves as a massless particle. When we take Y5 to be S5, we provide a microscopical description in terms of multiple gravitational waves expanding into the fuzzy S5 defined as an S1 bundle over the fuzzy CP2. Finally we provide a possible field theory dual interpretation of the construction.

Pp‐wave matrix models from point‐like gravitons

AbstractThe BFSS Matrix model can be regarded as a theory of coincident M‐theory gravitons. In this spirit, we summarize how using the action for coincident gravitons proposed in hep‐th/0207199 it is possible to go beyond the linear order approximation of Kabat and Taylor, and to provide a satisfactory microscopical description of giant gravitons in AdSm × Sn backgrounds. We then show that in the M‐theory maximally supersymmetric pp‐wave background, the action for coincident gravitons, besides reproducing the BMN Matrix model, predicts a new quadrupolar coupling to the M‐theory 6‐form potential, which supports the so far elusive fuzzy 5‐sphere giant graviton solution. Finally, we discuss similar Matrix models that can be derived in Type II string theories using dualities.

1/16-BPS black holes and giant gravitons in the AdS5× S5Space

We explore 1/16-BPS objects of type IIB string theory in AdS_5 * S^5. First, we consider supersymmetric AdS_5 black holes, which should be 1/16-BPS and have a characteristic that not all physical charges are independent. We point out that the Bekenstein-Hawking entropy of these black holes admits a remarkably simple expression in terms of (dependent) physical charges, which suggests its microscopic origin via certain Cardy or Hardy-Ramanujan formula. We also note that there is an upper bound for the angular momenta given by the electric charges. Second, we construct a class of 1/16-BPS giant graviton solutions in AdS_5 * S^5 and explore their properties. The solutions are given by the intersections of AdS_5 * S^5 and complex 3 dimensional holomorphic hyperspaces in C^{1+5}, the latter being the zero loci of three holomorphic functions which are homogeneous with suitable weights on coordinates. We investigate examples of giant gravitons, including their degenerations to tensionless strings.

Spinning string and giant graviton in electric/magnetic field deformedAdS3×S3×T4

We apply the transformation of the mixing azimuthal and internal coordinate or the mixing time and internal coordinate to the 11D M theory with a stack of $\mathrm{M}2\mathrm{\text{\ensuremath{-}}}\mathrm{branes}\ensuremath{\perp}\mathrm{M}2\mathrm{\text{\ensuremath{-}}}\mathrm{branes}$, then through the mechanism of Kaluza-Klein reduction and a series of the T duality we obtain the corresponding background of a stack of $\mathrm{D}1\mathrm{\text{\ensuremath{-}}}\mathrm{branes}\ensuremath{\perp}\mathrm{D}5\mathrm{\text{\ensuremath{-}}}\mathrm{branes}$ which, in the near-horizon limit, becomes the magnetic or electric Melvin field deformed ${\mathrm{AdS}}_{3}\ifmmode\times\else\texttimes\fi{}{S}^{3}\ifmmode\times\else\texttimes\fi{}{T}^{4}$. We find the giant graviton solution in the deformed spacetime and see that the configuration whose angular momentum is within a finite region could have a fixed size and become more stable than the pointlike graviton, in contrast to the undeformed giant graviton which only exists when its angular momentum is a specific value and could have arbitrary size. We discuss in detail the properties of how the electric/magnetic Melvin field will affect the size of the giant gravitons. We also adopt an ansatz to find the classical string solutions which are rotating in the deformed ${S}^{3}$ with an angular momentum in the rotation plane. The spinning string and giant graviton solutions we obtained show that the external magnetic/electric flux will increase the solution energy. Therefore, from the anti-de Sitter (AdS)/conformal field theory (CFT) point of view, the corrections of the anomalous dimensions of operators in the dual field theory will be positive. Finally, we also see that the spinning string and giant graviton in the near-horizon spacetime of Melvin field deformed D5-branes background have similar properties to those in the deformed ${\mathrm{AdS}}_{3}\ifmmode\times\else\texttimes\fi{}{S}^{3}\ifmmode\times\else\texttimes\fi{}{T}^{4}$.

Unstable giant gravitons

We find giant graviton solutions in Frolov's three parameter generalization of the Lunin-Maldacena background. The background we study has $\tilde{\gamma}_1=0$ and $\tilde{\gamma}_2=\tilde{\gamma}_3=\tilde{\gamma}$. This class of backgrounds provide a non-superymmetric example of the gauge theory/gravity correspondence that can be tested quantitatively, as recently shown by Frolov, Roiban and Tseytlin. The giant graviton solutions we find have a greater energy than the point gravitons, making them unstable states. Despite this, we find striking quantitative agreement between the gauge theory and gravity descriptions of open strings attached to the giant.

BPS electromagnetic waves on giant gravitons

We find new 1/8-BPS giant graviton solutions in $AdS_5 \times S^5$, carrying three angular momenta along $S^5$, and investigate their properties. Especially, we show that nonzero worldvolume gauge fields are admitted preserving supersymmetry. These gauge field modes can be viewed as electromagnetic waves along the compact D3 brane, whose Poynting vector contributes to the BPS angular momenta. We also analyze the (nearly-)spherical giant gravitons with worldvolume gauge fields in detail. Expressing the $S^3$ in Hopf fibration ($S^1$ fibred over $S^2$), the wave propagates along the $S^1$ fiber.

1/2BPS geometries of M2 giant gravitons

We construct the general $1/2$ BPS M2 giant graviton solutions asymptotic to the 11-dimensional maximally supersymmetric plane-wave background, based on the recent work of Lin, Lunin, and Maldacena. The solutions have null singularity and we argue that it is unavoidable to have null singularity in the proposed framework, although the solutions are still physically relevant. They involve an arbitrary function $F(x)$ which is shown to have a correspondence to the $1/2$ BPS states of the Berenstein-Maldacena-Nastase (BMN) matrix model. A detailed map between the $1/2$ BPS states of both sides is worked out.

Fuzzy 5-spheres and pp-wave Matrix actions

Using the action describing N coincident gravitational waves in M-theory we construct a pp-wave Matrix model cointaning a fuzzy 5-sphere giant graviton solution. This fuzzy 5-sphere is constructed as a U(1) fibration over a fuzzy $CP^2$, and has the correct dependence of the radius with the light-cone momentum, $r^4\sim p^+$, to approach the 5-sphere giant graviton solution of Mc.Greevy et al in the large N limit.

What is the gravity dual of a chiral primary?

In the AdS/CFT correspondence a chiral primary is described by a string theory solution with mass equaling angular momentum. For AdS 3× S 3 we are led to consider three special families of metrics with this property: metrics with conical defects, Aichelburg–Sexl type metrics generated by rotating particles, and metrics generated by giant gravitons. We find that the first two of these are special cases of the complete family of chiral primary metrics which can be written down using the general solution in hep-th/0109154, but they correspond to two extreme limits—the conical defect metrics map to CFT states generated by twist operators that are all identical, while the Aichelburg–Sexl metrics yield a wide dispersion in the orders of these twists. The giant graviton solutions in contrast do not represent configurations of the D1–D5 bound state; they correspond to fragmenting this system into two or more pieces. We look at the large distance behavior of the supergravity fields and observe that the excitation of these fields is linked to the existence of dispersion in the orders and spins of the twist operators creating the chiral primary in the CFT.