arXiv subjects

Samir D. Mathur

Publications and source records attributed to Samir D. Mathur.

At least 127 records · Page 7Linked to original sources

arXiv2001

Three-point functions for M^N/S^N orbifolds with N=4 supersymmetry

The D1-D5 system is believed to have an `orbifold point' in its moduli space where its low energy theory is a N=4 supersymmetric sigma model with target space M^N/S^N, where M is T^4 or K3. We study correlation functions of chiral operators in CFTs arising from such a theory. We construct a basic class of chiral operators from twist fields of the symmetric group and the generators of the superconformal algebra. We find explicitly the 3-point functions for these chiral fields at large N; these expressions are `universal' in that they are independent of the choice of M. We observe that the result is a significantly simpler expression than the corresponding expression for the bosonic theory based on the same orbifold target space.

hep-th↗

arXiv2000

Correlation functions for M^N/S_N orbifolds

We develop a method for computing correlation functions of twist operators in the bosonic 2-d CFT arising from orbifolds M^N/S_N, where M is an arbitrary manifold. The path integral with twist operators is replaced by a path integral on a covering space with no operator insertions. Thus, even though the CFT is defined on the sphere, the correlators are expressed in terms of partition functions on Riemann surfaces with a finite range of genus g. For large N, this genus expansion coincides with a 1/N expansion. The contribution from the covering space of genus zero is `universal' in the sense that it depends only on the central charge of the CFT. For 3-point functions we give an explicit form for the contribution from the sphere, and for the 4-point function we do an example which has genus zero and genus one contributions. The condition for the genus zero contribution to the 3-point functions to be non--vanishing is similar to the fusion rules for an SU(2) WZW model. We observe that the 3-point coupling becomes small compared to its large N limit when the orders of the twist operators become comparable to the square root of N - this is a manifestation of the stringy exclusion principle.

hep-th↗

arXiv2000

Giant Gravitons, BPS bounds and Noncommutativity

It has been recently suggested that gravitons moving in $AdS_m \times S^n$ spacetimes along the $S^n$ blow up into spherical $(n-2)$ branes whose radius increases with increasing angular momentum. This leads to an upper bound on the angular momentum, thus ``explaining'' the stringy exclusion principle. We show that this bound is present only for states which saturate a BPS-like condition involving the energy $E$ and angular momentum $J$, $E \geq J/R$, where $R$ is the radius of $S^n$. Restriction of motion to such states lead to a noncommutativity of the coordinates on $S^n$. As an example of motions which do not obey the exclusion principle bound, we show that there are finite action instanton configurations interpolating between two possible BPS states. We suggest that this is consistent with the proposal that there is an effective description in terms of supergravity defined on noncommutative spaces and noncommutativity arises here because of imposing supersymmetry.

hep-th↗

arXiv2000

Vibration modes of giant gravitons

We examine the spectrum of small vibrations of giant gravitons, when the gravitons expand in the anti-de-Sitter space and when they expand on the sphere. For any given angular harmonic, the modes are found to have frequencies related to the curvature length scale of the background; these frequencies are independent of radius (and hence angular momentum) of the brane itself. This implies that the holographic dual theory must have, in a given R charge sector, low-lying non-BPS excitations with level spacings independent of the R charge.

hep-th↗

arXiv2000

Resolving the black hole information paradox

The recent progress in string theory strongly suggests that formation and evaporation of black holes is a unitary process. This fact makes it imperative that we find a flaw in the semiclassical reasoning that implies a loss of information. We propose a new criterion that limits the domain of classical gravity: the hypersurfaces of a foliation cannot be stretched too much. This conjectured criterion may have important consequences for the early Universe.

gr-qc↗

arXiv2000

From Black Holes to Pomeron: Tensor Glueball and Pomeron Intercept at Strong Coupling

We briefly review the approach for strong coupling calculation of glueball masses based on the duality between supergravity and Yang-Mills theory. Earlier work is extended to non-zero spin. Fluctuations in the gravitational metric lead to the $2^{++}$ tensor glueball state on the leading Pomeron trajectory with a mass relation: $m(0^{++}) < m(2^{++}) $. In particular, for $QCD_4$, a strong coupling expansion for the Pomeron intercept is obtained.

hep-ph↗

arXiv2000

Glueball Spectrum for QCD from AdS Supergravity Duality

We present the analysis of the complete glueball spectrum for the $AdS^7$ black hole supergravity dual of $QCD_4$ in strong coupling limit: $g^2 N \to \infty$. The bosonic fields in the supergravity multiplet lead to 6 independent wave equations contributing to glueball states with $J^{PC} = 2^{++},1^{+-}, 1^{--}$, $0^{++}$ and $0^{-+}$. We study the spectral splitting and degeneracy patterns for both $QCD_4$ and $QCD_3$. Despite the expected limitations of a leading order strong coupling approximation, the pattern of spins, parities and mass inequalities bear a striking resemblance to the known $QCD_4$ glueball spectrum as determined by lattice simulations at weak coupling.

hep-th↗

arXiv1999

The Operator Product Expansion of N=4 SYM and the 4-point Functions of Supergravity

We give a detailed Operator Product Expansion interpretation of the results for conformal 4-point functions computed from supergravity through the AdS/CFT duality. We show that for an arbitrary scalar exchange in AdS(d+1) all the power-singular terms in the direct channel limit (and only these terms) exactly match the corresponding contributions to the OPE of the operator dual to the exchanged bulk field and of its conformal descendents. The leading logarithmic singularities in the 4-point functions of protected N=4 super-Yang Mills operators (computed from IIB supergravity on AdS(5) X S(5) are interpreted as O(1/N^2) renormalization effects of the double-trace products appearing in the OPE. Applied to the 4-point functions of the operators Ophi ~ tr F^2 + ... and Oc ~ tr FF~ + ..., this analysis leads to the prediction that the double-trace composites [Ophi Oc] and [Ophi Ophi - Oc Oc] have anomalous dimension -16/N^2 in the large N, large g_{YM}^2 N limit. We describe a geometric picture of the OPE in the dual gravitational theory, for both the power-singular terms and the leading logarithms. We comment on several possible extensions of our results.

hep-th↗

arXiv1999

From Black Holes to Glueballs: The QCD_3 Tensor Glueball at Strong Coupling

A strong coupling calculation of glueball masses based on the duality between supergravity and Yang-Mills theory is presented. Earlier work is extended to non-zero spin. Fluctuations in the gravitational metric lead to the 2^{++} state on the leading Pomeron trajectory with a mass relation: m(0^{++}) < m(2^{++}) < m(1^{-+}). Contrary to expectation, the mass of our new 0^{++} state (m^2=5.4573) associated with the graviton is smaller than the mass of the ${\tilde 0}^{++}$ state (m^2=11.588) from the dilaton, which in fact is exactly degenerate with the tensor 2^{++}.

hep-lat↗

arXiv1999

Discrete Spectrum of the Graviton in the $AdS^5$ Black Hole Background

The discrete spectrum of fluctuations of the metric about an $AdS^5$ black hole background are found. These modes are the strong coupling limit of so called glueball states in a dual 3-d Yang-Mills theory with quantum numbers $J^{PC} = 2^{++}, 1^{-+}, 0^{++}$. For the ground state modes, we find the mass relation: $m(0^{++}) < m(2^{++}) < m(1^{-+})$. Contrary to expectation, the mass of our new $0^{++}$ state ($m^2=5.4573$) associated with the graviton is smaller than the mass of the $0^{++}$ state ($m^2=11.588$) from the dilaton. In fact the dilatonic excitations are exactly degenerate with our tensor $2^{++}$ states. We find that variational methods gives remarkably accurate mass estimates for all three low-lying levels while a WKB treatment describes the higher modes well.

hep-th↗

arXiv1999

Graviton exchange and complete 4-point functions in the AdS/CFT correspondence

The graviton exchange diagram for the correlation function of arbitrary scalar operators is evaluated in anti-de Sitter space, AdS(d+1). This enables us to complete the computation of the 4-point amplitudes of dilaton and axion fields in IIB supergravity on AdS5 X S5. By the AdS/CFT correspondence, we obtain the 4-point functions of the marginal operators Tr (F^2+...) and Tr(F F~ +...) in N=4, d=4 SU(N) SYM at large N, large g^2 N. The short distance asymptotics of the amplitudes are studied. We find that in the direct channel the leading power singularity agrees with the expected contribution of the stress-energy tensor in a double OPE expansion. Logarithmic singularities occur in the complete 4-point functions at subleading orders.

hep-th↗

arXiv1999

Graviton and gauge boson propagators in AdS(d+1)

We construct the gauge field and graviton propagators in Euclidean AdS(d+1) space-time by two different methods. In the first method the gauge invariant Maxwell or linearized Ricci operator is applied directly to bitensor ansatze for the propagators which reflect their gauge structure. This leads to a rapid determination of the physical part of the propagators in terms of elementary functions. The second method is a more traditional approach using covariant gauge fixing which leads to a solution for both physical and gauge parts of the propagators. The gauge invariant parts agree in both methods.

hep-th↗

arXiv1998

Absorption of partial waves by three-branes

We study the absorption of a class of fields in the geometry produced by extremal three-branes. We consider fields that do not mix with the ten-dimensional graviton. For these fields we solve the wave equations and find the absorption probabilities for all partial waves at leading order in the energy. We note that in some of these cases one needs an `intermediate' region which interpolates between flat Minkowski space at infinity and the AdS geometry near the branes.

hep-th↗

arXiv1998

Comments on 4-point functions in the CFT/AdS correspondence

We study the four--point function of chiral primaries corresponding to the dilaton--axion sector in supergravity in the $AdS_5$/CFT$_4$ correspondence. We find relations between some of the supergravity graphs and compute their leading singularities. We discuss the issue of logarithmic singularities and their significance for the OPE structure of the CFT.

hep-th↗

arXiv1998

Correlation functions in the CFT(d)/AdS(d+1) correpondence

Conformal techniques are applied to the calculation of integrals on AdS(d+1) space which define correlators of composite operators in the superconformal field theory on the d-dimensional boundary. The 3-point amplitudes for scalar fields of arbitrary mass and gauge fields in the AdS supergravity are calculated explicitly. For 3 gauge fields we compare in detail with the known conformal structure of the SU(4) flavor current correlator of the N=4, d=4 SU(N) SYM theory. Results agree with the free field approximation as would be expected from superconformal non-renormalization theorems. In studying the Ward identity relating to for (non-marginal) scalar composite operators O^I, we find that there is a subtlety in obtaining the normalization of from the supergravity action integral.

hep-th↗

arXiv1998

Hawking Radiation from Four-dimensional Schwarzschild Black Holes in M-theory

Recently a method has been developed for relating four dimensional Schwarzschild black holes in M-theory to near-extremal black holes in string theory with four charges, using suitably defined ``boosts'' and T-dualities. We show that this method can be extended to obtain the emission rate of low energy massless scalars for the four dimensional Schwarzschild hole from the microscopic picture of radiation from the near extremal hole.

hep-th↗

arXiv1997

Boosts, Schwarzschild Black Holes and Absorption cross-sections in M theory

$D$ dimensional neutral black strings wrapped on a circle are related to $(D-1)$ dimensional charged black holes by boosts. We show that the boost has to be performed in the covering space and the boosted coordinate has to be compactified on a circle with a Lorentz contracted radius. Using this fact we show that the transition between Schwarzschild black holes to black p-branes observed recently in M theory is the well-known black hole- black string transition viewed in a boosted frame. In a similar way the correspondence point where an excited string state goes over to a neutral black hole is mapped exactly to the correspondence point for black p-branes. In terms of the $p$ brane quantities the equation of state for an excited string state becomes identical to that of a 3+1 dimensional massless gas for all $p$. Finally, we show how boosts can be used to relate Hawking radiation rates. Using the known microscopic derivation of absorption by extremal 3-branes and near-extremal 5D holes with three large charges we provide a microscopic derivation of absorption of 0-branes by seven and five dimensional Schwarzschild black holes in a certain regime.

hep-th↗

arXiv1997

Supersymmetry and Membrane Interactions in M(atrix) Theory

We calculate the potential between various configurations of membranes and gravitons in M(atrix) theory. The computed potentials agree with the short distance potentials between corresponding 2-branes and 0-brane configurations in Type IIA string theory, bound to a large number of 0-branes to account for the boost to the infinite momentum frame. We show that, due to the large boost, these type IIA configurations are almost supersymmetric, so that the short and long distance potentials actually agree. Thus the M(atrix) theory is able to reproduce correct long distance behavior in these cases.

hep-th↗