Dan Tomino

Quantum corrections on fuzzy sphere

We investigate quantum corrections in non-commutative gauge theory on fuzzy sphere. We study translation invariant models which classically favor a single fuzzy sphere with U(1) gauge group. We evaluate the effective actions up to the two-loop level. We find non-vanishing quantum corrections at each order even in supersymmetric models. In particular the two-loop contribution favors U(n) gauge group over U(1) contrary to the tree action in a deformed IIB matrix model with a Myers term. We further observe close correspondences to 2-dimensional quantum gravity.

Drag force in SYM plasma with B field from AdS/CFT

We investigate drag force in a thermal plasma of N=4 super Yang-Mills theory via both fundamental and Dirichlet strings under the influence of non-zero NSNS B-field background. In the description of AdS/CFT correspondence the endpoint of these strings correspondes to an external monopole or quark moving with a constant electromagnetic field. We demonstrate how the configuration of string tail as well as the drag force obtains corrections in this background.

Stability of fuzzy S2×S2×S2 in IIB type matrix models

We study the stability of fuzzy S^2 x S^2 x S^2 backgrounds in three different IIB type matrix models with respect to the change of the spins of each S^2 at the two loop level. We find that S^2 x S^2 x S^2 background is metastable and the effective action favors a single large S^2 in comparison to the remaining S^2 x S^2 in the models with Myers term. On the other hand, we find that a large S^2 x S^2 in comparison to the remaining S^2 is favored in IIB matrix model itself. We further study the stability of fuzzy S^2 x S^2 background in detail in IIB matrix model with respect to the scale factors of each S^2 as well. In this case, we find unstable directions which lower the effective action away from the most symmetric fuzzy S^2 x S^2 background.

Supersymmetric reduced models with a symmetry based on Filippov algebra

Generalizations of the reduced model of super Yang-Mills theory obtained by replacing the Lie algebra structure to Filippov n-algebra structures are studied. Conditions for the reduced model actions to be supersymmetric are examined. These models are related with what we call min = 2 super p-brane actions.

Hagedorn strings and correspondence principle in AdS3

Motivated by the possibility of formulating a strings/black hole correspondence in AdS space, we extract the Hagedorn behavior of thermal AdS3 bosonic string from 1-loop partition function of SL(2, R) WZW model. We find that the Hagedorn temperature is monotonically increasing as the AdS radius shrinks, reaches a maximum of order of string scale set by the unitarity bound of the CFT for internal space. The resulting density of states near the Hagedorn temperature resembles the form as for strings in flat space and is dominated by the space-like long string configurations. We then argue a conjectured strings/black hole correspondence in AdS space by applying the Hagedorn thermodynamics. We find the size of the corresponding black hole is a function of the AdS radius. For large AdS radius a black hole far bigger than the string scale will form. On the contrary, when the AdS and string scales are comparable a string size black hole will form. We also examine strings on BTZ background obtained through SL(2, Z) transformation. We find a tachyonic divergence for a BTZ black hole of string scale size.

Correlators of matrix models on homogeneous spaces

Abstract We investigate the correlators of Tr A μ A ν in matrix models on homogeneous spaces: S 2 and S 2 × S 2 . Their expectation value is a good order parameter to measure the geometry of the space on which non-commutative gauge theory is realized. They also serve as the Wilson lines which carry the minimum momentum. We develop an efficient procedure to calculate them through 1PI diagrams. We determine the large N scaling behavior of the correlators. The order parameter shows that fuzzy S 2 × S 2 acquires a 4-dimensional fractal structure in contrast to fuzzy S 2 . We also find that the two point functions exhibit logarithmic scaling violations.

Fuzzy spacetime with SU(3) isometry in the IIB matrix model

A group of fuzzy spacetime with SU(3) isometry is studied at the two-loop level in a IIB matrix model. It consists of spacetime from four to six dimensions, namely, from CP{sup 2} to SU(3)/U(1)xU(1). The effective action scales in a universal manner in the large N limit as N and N{sup 4/3} on four- and six-dimensional manifolds, respectively. The four-dimensional spacetime CP{sup 2} possesses the smallest effective action in this class.

N = 2 3d-matrix integral with Myers term

An exact matrix integral is evaluated for a 2 × 2 3-dimensional matrix model with Myers term. We derive weak and strong coupling expansions of the effective action. We also calculate the expectation values of the quadratic and cubic operators. Implications for non-commutative gauge theory on fuzzy sphere are discussed.

Quasinormal modes of Kerr black holes in four and higher dimensions

We analytically calculate to leading order the asymptotic form of quasinormal frequencies of Kerr black holes in four, five, and seven dimensions. All the relevant quantities can be explicitly expressed in terms of elliptical integrals. In four dimensions, we confirm the results obtained by Keshest and Hod by comparing the analytic results to the numerical ones.

Wilson line correlators in N=4 non-commutative gauge theory on S2×S2

We investigate the Wilson line correlators dual to supergravity multiplets in N=4 non-commutative gauge theory on S^2 x S^2. We find additional non-analytic contributions to the correlators due to UV/IR mixing in comparison to ordinary gauge theory. Although they are no longer BPS off shell, their renormalization effects are finite as long as they carry finite momenta. We propose a renormalization procedure to obtain local operators with no anomalous dimensions in perturbation theory. We reflect on our results from dual supergravity point of view. We show that supergravity can account for both IR and UV/IR contributions.