A Self-tuning Exact Solution and the Non-existence of Horizons in 5d Gravity-Scalar System

We present an exact thick domain wall solution with naked sigularities to five dimensional gravity coupled with a scalar field with exponential potential. In our solution we found exactly the special coefficient of the exponent as coming from compactification of string theory with cosmological constant. We show that this solution is self-tuning when a 3-brane is included. In searching for solution with horizon we found a similar exact solution with fine-tuned exponent coefficient with an integration constant. Failed to find a solution with horizon we prove the non-existence of horizons. These naked sigularities actually can't be resolved by horizon. We also comment on the physical relevance of this solution.}Comment: 15 pages, 1 figure, Latex with epsf.tex; v2, pen mistakes corrected, one refreence added; v3, grammar errors corrected, to appear in JHE

Instantons on General Noncommutative R^4

We study the U(1) and U(2) instanton solutions of gauge theory on general noncommutative $\bf{R}^4$. In all cases considered we obtain explicit results for the projection operators. In some cases we computed numerically the instanton charge and found that it is an integer, independent of the noncommutative parameters $\theta_{1,2}$.Comment: 14 pages, LaTeX; deleted some confusing statements in the U(1) 1-instanton case, added ref

Explicit Modular Invariant Two-Loop Superstring Amplitude Relevant for R^4

In this note we derive an explicit modular invariant formula for the two loop 4-point amplitude in superstring theory in terms of a multiple integral (7 complex integration variables) over the complex plane which is shown to be convergent. We consider in particular the case of the leading term for vanishing momenta of the four graviton amplitude, which would correspond to the two-loop correction of the R^4 term in the effective Action. The resulting expression is not positive definite and could be zero, although we cannot see that it vanishes.Comment: 18 pages, the introduction (2.5 pages) is a comprehensive summary including the main resul

The Complete Brane Solution in D-dimensional Coupled Gravity System

In this letter we present the complete explicit brane solution in D-dimensional coupled gravity system.Comment: 6 pages, Latex, no figurer