Non-perturbative RR potentials in the ĉ=1 matrix model - Gross, David; Walcher, Johannes (Journal of high energy physics, 2004)
We use the ##IMG## [http://ej.iop.org/icons/Entities/hatc.gif] hat c = 1 matrix model to compute the potential energy V ( C ) for (the zero mode of) the RR scalar in two-dimensional type 0B string theory. The potential is induced by turning on a background RR flux, which in the matrix model corresponds to unequal Fermi levels for the two types of fermions. Perturbatively, this leads to a linear runaway potential, but non-perturbative effects stabilize the potential, and we find the exact expression V ( C ) = (1/2π) ∫ da arccos [cos ( C )/(1+e −2π a ) 1/2 ]. We also compute the finite-temperature partition function of the 0B theory in the presence of flux. The perturbative expansion is T-dual to the analogous result in type 0A theory, but non-perturbative effects (which depend on C ) do not respect naive R →1/ R duality. The model can also be used to study scattering amplitudes in background RR fluxes.