Orbifold equivalence and the sign problem at finite baryon density.

We point out that SO(2N(c)) gauge theory with N(f) fundamental Dirac fermions does not have a sign problem at finite baryon number chemical potential µ(B). One can thus use lattice Monte Carlo simulations to study this theory at finite density. The absence of a sign problem in the SO(2N(c)) theory is particularly interesting because a wide class of observables in the SO(2N(c)) theory coincide with observables in QCD in the large N(c) limit, as we show using the technique of large N(c) orbifold equivalence. We argue that the orbifold equivalence between the two theories continues to hold at finite µ(B) provided one adds appropriate deformation terms to the SO(2N(c)) theory. This opens up the prospect of learning about QCD at finite µ(B) using lattice studies of the SO(2N(c)) theory.

Nonperturbative corrections to 4D string theory effective actions from SL(2,Z) duality and supersymmetry.

We find the D(-1)- and D1-brane instanton contributions to the hypermultiplet moduli space of type IIB string compactifications on Calabi-Yau threefolds. These combine with known perturbative and world sheet instanton corrections into a single modular invariant function that determines the hypermultiplet low-energy effective action.