We revisit the evaluation of one-loop modular integrals in string theory, employing new methods that, unlike the traditional orbit method, keep T-duality manifest throughout. In particular, we apply the Rankin-Selberg-Zagier approach to cases where t
he integrand function grows at most polynomially in the IR. Furthermore, we introduce new techniques in the case where `unphysical tachyons contribute to the one-loop couplings. These methods can be viewed as a modular invariant version of dimensional regularisation. As an example, we treat one-loop BPS-saturated couplings involving the $d$-dimensional Narain lattice and the invariant Klein $j$-function, and relate them to (shifted) constrained Epstein Zeta series of O(d,d;Z). In particular, we recover the well-known results for d=2 in a few easy steps.
The three generation heterotic-string models in the free fermionic formulation are among the most realistic string vacua constructed to date, which motivated their detailed investigation. The classification of free fermion heterotic string vacua has
revealed a duality under the exchange of spinor and vector representations of the SO(10) GUT symmetry over the space of models. We demonstrate the existence of the spinor-vector duality using orbifold techniques, and elaborate on the relation of these vacua to free fermionic models.
We compute instantonic effects in globally consistent T^6/Z2xZ2 orientifold models with discrete torsion and magnetised D-branes. We consider fractional branes and instantons wrapping the same rigid cycles. We clarify and analyse in detail the low-en
ergy effective action on D-branes in these models. We provide explicit examples where instantons induce linear terms in the charged fields, or non-perturbative mass terms are generated. We also find examples where the gauge theory on fractional branes has conformal symmetry at one-loop, broken by instantonic mass terms at a hierarchically small energy scale.
We consider closed type II and orientifold backgrounds where supersymmetry is spontaneously broken by asymmetric geometrical fluxes. We show that these can be used to describe thermal ensembles with chemical potentials associated to gravito-magnetic
fluxes. The thermal free energy is computed at the one-loop string level, and it is shown to be free of the usual Hagedorn-like instabilities for a certain choice of the chemical potentials. In the closed string gravitational sector, as well as in the open string matter sector of the proposed orientifold construction, the free energy turns out to have Temperature duality symmetry, ${cal F}(T/T_H)={T^2over T_H^2} {cal F}(T_H/T)$, which requires interchanging the space-time spinor representations $Sleftrightarrow C$. For small temperatures, $Tto 0$, the anti-spinor $C$ decouples from the spectrum while for large temperatures, $Tto infty$, the spinor $S$ decouples. In both limits the free energy vanishes, as we recover a conventional type II superstring theory. At the self dual point $T=T_H$, the thermal spectra of $S$ and $C$ are identical. Moreover, there are extra massless scalars in the adjoint representation of an SO(4) non-abelian gauge symmetry in the closed-string sector, and open-string massless states charged simultaneously under both the Chan-Paton and the closed-string SO(4) gauge group.
We argue that tachyon-free type I string vacua with supersymmetry breaking in the open sector at the string scale can be interpreted, via S and T-duality arguments, as metastable vacua of supersymmetric type I superstring. The dynamics of the process
can be partially captured via nucleation of brane-antibrane pairs out of the non-supersymmetric vacuum and subsequent tachyon condensation.
