Decoupling a Fermion Whose Mass Comes from a Yukawa Coupling: Nonperturbative Considerations

Perturbative analyses seem to suggest that fermions whose mass comes solely from a Yukawa coupling to a scalar field can be made arbitrarily heavy, while the scalar remains light. The effects of the fermion can be summarized by a local effective Lagrangian for the light degrees of freedom. Using weak coupling and large N techniques, we present a variety of models in which this conclusion is shown to be false when nonperturbative variations of the scalar field are considered. The heavy fermions contribute nonlocal terms to the effective action for light degrees of freedom. This resolves paradoxes about anomalous and nonanomalous symmetry violation in these models. Application of these results to lattice gauge theory imply that attempts to decouple lattice fermion doubles by the method of Swift and Smit cannot succeed, a result already suggested by lattice calculations.Comment: 31 page

String Islands

We discuss string theories with small numbers of non-compact moduli and describe constructions of string theories whose low-energy limit is described by various pure supergravity theories. We also construct a D=4,N=4 compactification of type II string theory with 34 vector fields.Comment: An erroneous example removed. We thank Massimo Bianchi and Cumrun Vafa for pointing out this erro

Two Centered Black Holes and N=4 Dyon Spectrum

The exact spectrum of dyons in a class of N=4 supersymmetric string theories is known to change discontinuously across walls of marginal stability. We show that the change in the degeneracy across the walls of marginal stability can be accounted for precisely by the entropy of two centered small black holes which disappear as we cross the walls of marginal stability.Comment: LaTeX file, 12 pages; v3: added footnote 2 regarding overall sign of the index, expanded footnote 3, added reference

Closed String Tachyons on C/Z_N

We analyse the condensation of closed string tachyons on the $C/Z_N$ orbifold. We construct the potential for the tachyons upto the quartic interaction term in the large $N$ limit. In this limit there are near marginal tachyons. The quartic coupling for these tachyons is calculated by subtracting from the string theory amplitude for the tachyons, the contributions from the massless exchanges, computed from the effective field theory. We argue that higher point interaction terms are are also of the same order in 1/N as the quartic term and are necessary for existence of the minimum of the tachyon potential that is consistent with earlier analysis.Comment: 19 pages, 1 figure; comments added about $N$ dependence of contact ter

Walls of Marginal Stability and Dyon Spectrum in N=4 Supersymmetric String Theories

The spectrum of quarter BPS dyons in N=4 supersymmetric string theories can change as the asymptotic moduli cross walls of marginal stability on which the dyon can break apart into a pair of half BPS states. In this paper we classify these marginal stability walls and examine this phenomenon in the context of exact dyon spectrum found in a class of N=4 supersymmetric string theories. We argue that the dyon partition functions in different domains separated by marginal stability walls are the same, but the choice of integration contour needed for extracting the degeneracies from the partition function differ in these different regions. We also find that in the limit of large charges the change in the degeneracy is exponentially suppressed compared to the leading contribution. This is consistent with the fact that in the computation of black hole entropy we do not encounter any change as the asymptotic moduli fields move across the walls of marginal stability. Finally we carry out some tests of S-duality invariance in the theory.Comment: LateX file, 1 figure, 42 pages; v2 more tests of S-duality added with complete proof for all N<7; v3: minor change

Adding Charges to N=4 Dyons

The spectrum of dyons in a class of N=4 supersymmetric string theories has been found for a specific set of electric and magnetic charge vectors. We extend the analysis to more general charge vectors by considering various charge carrying collective excitations of the original system.Comment: LaTeX file, 16 page

Violating the string winding number maximally in Anti-de Sitter space

We study n-string scattering amplitudes in three-dimensional Anti-de Sitter space (AdS3). We focus our attention on the processes in which the winding number conservation is violated maximally; that is, those processes in which it is violated in n-2 units. A worldsheet conformal field theory calculation leads us to confirm a previous conjecture about the functional form of these observables.Comment: 15 pages. V2 references added and minor typo corrected. V3, V4 addendum on an alternative derivation of the main formula for short string

Higher Derivative Corrections, Dimensional Reduction and Ehlers Duality

Motivated by applications to black hole physics and duality, we study the effect of higher derivative corrections on the dimensional reduction of four-dimensional Einstein, Einstein Liouville and Einstein-Maxwell gravity to one direction, as appropriate for stationary, spherically symmetric solutions. We construct a field redefinition scheme such that the one-dimensional Lagrangian is corrected only by powers of first derivatives of the fields, eliminating spurious modes and providing a suitable starting point for quantization. We show that the Ehlers symmetry, broken by the leading $R^2$ corrections in Einstein-Liouville gravity, can be restored by including contributions of Taub-NUT instantons. Finally, we give a preliminary discussion of the duality between higher-derivative F-term corrections on the vector and hypermultiplet branches in N=2 supergravity in four dimensions.Comment: 21 pages, uses JHEP3.cls; v3: minor corrections, final version published in JHE

Negative discriminant states in N=4 supersymmetric string theories

Single centered BPS black hole solutions exist only when the charge carried by the black hole has positive discriminant. On the other hand the exact dyon spectrum in heterotic string theory compactified on T^6 is known to contain states with negative discriminant. We show that all of these negative discriminant states can be accounted for as two centered black holes. Thus after the contribution to the index from the two centered black holes is subtracted from the total microscopic index, the index for states with negative discriminant vanishes even for finite values of charges, in agreement with the results from the black hole side. Bound state metamorphosis -- which requires us to identify certain apparently different two centered configurations according to a specific set of rules -- plays a crucial role in this analysis. We also generalize these results to a class of CHL string theories.Comment: LaTeX file, 32 pages; v2: reference added; v3: added new section 3.