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

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. 1

We evaluate the effective actions of supersymmetric matrix models on fuzzy S 2 × S 2 up to the two loop level. Remarkably it turns out to be a consistent solution of IIB matrix model. Based on the power counting and SUSY cancellation arguments, we can identify the 't Hooft coupling and large N scaling behavior of the effective actions to all orders. In the large N limit, the quantum corrections survive except in 2 dimensional limits. They are O(N ) and O(N 4 3 ) for 4 and 6 dimensional spaces respectively. We argue that quantum effects single out 4 dimensionality among fuzzy homogeneous spaces.

We investigate the correlators of T rA 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.

Motivated by the possibility of formulating a strings/black hole correspondence in AdS space, we extract the Hagedorn behavior of thermal AdS 3 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. 1