Large N and double scaling limits in two dimensions

Recently, the author has constructed a series of four dimensional non-critical string theories with eight supercharges, dual to theories of light electric and magnetic charges, for which exact formulas for the central charge of the space-time supersymmetry algebra as a function of the world-sheet couplings were obtained. The basic idea was to generalize the old matrix model approach, replacing the simple matrix integrals by the four dimensional matrix path integrals of N=2 supersymmetric Yang-Mills theory, and the Kazakov critical points by the Argyres-Douglas critical points. In the present paper, we study qualitatively similar toy path integrals corresponding to the two dimensional N=2 supersymmetric non-linear sigma model with target space CP^n and twisted mass terms. This theory has some very strong similarities with N=2 super Yang-Mills, including the presence of critical points in the vicinity of which the large n expansion is IR divergent. The model being exactly solvable at large n, we can study non-BPS observables and give full proofs that double scaling limits exist and correspond to universal continuum limits. A complete characterization of the double scaled theories is given. We find evidence for dimensional transmutation of the string coupling in some non-critical string theories. We also identify en passant some non-BPS particles that become massless at the singularities in addition to the usual BPS states.Comment: 38 pages, including an introductory section that makes the paper self-contained, two figures and one appendix; v2: typos correcte

A geometric bound on F-term inflation

We discuss a general bound on the possibility to realise inflation in any minimal supergravity with F-terms. The derivation crucially depends on the sGoldstini, the scalar field directions that are singled out by spontaneous supersymmetry breaking. The resulting bound involves both slow-roll parameters and the geometry of the K\"ahler manifold of the chiral scalars. We analyse the inflationary implications of this bound, and in particular discuss to what extent the requirements of single field and slow-roll can both be met in F-term inflation.Comment: 14 pages, improved analysis, references added, matches published versio

Higher Loop Spin Field Correlators in D=4 Superstring Theory

We develop calculational tools to determine higher loop superstring correlators involving massless fermionic and spin fields in four space time dimensions. These correlation functions are basic ingredients for the calculation of loop amplitudes involving both bosons and fermions in D=4 heterotic and superstring theories. To obtain the full amplitudes in Lorentz covariant form the loop correlators of fermionic and spin fields have to be expressed in terms of SO(1,3) tensors. This is one of the main achievements in this work.Comment: 59 pages, 1 figure; v2: final version published in JHE

Critical Collapse in the Axion-Dilaton System in Diverse Dimensions

We study the gravitational collapse of the axion-dilaton system suggested by type IIB string theory in dimensions ranging from four to ten. We extend previous analysis concerning the role played by the global SL(2,R) symmetry and we evaluate the Choptuik exponents in the elliptic case.Comment: LaTeX, 10 pages, no figure

A Minimal Inflation Scenario

We elaborate on a minimal inflation scenario based entirely on the general properties of supersymmetry breaking in supergravity models. We identify the inflaton as the scalar component of the Goldstino superfield. We write plausible candidates for the effective action describing this chiral superfield. In particular the theory depends (apart from parameters of O(1)) on a single free parameter: the scale of supersymmetry breaking. This can be fixed using the amplitude of CMB cosmological perturbations and we therefore obtain the scale of supersymmetry breaking to be 10^{12-14} GeV. The model also incorporates explicit R-symmetry breaking in order to satisfy the slow roll conditions. In our model the eta-problem is solved without extra fine-tuning. We try to obtain as much information as possible in a model independent way using general symmetry properties of the theory's effective action, this leads to a new proposal on how to exit the inflationary phase and reheat the Universe.Comment: matches published version (typo corrected

Riemannian Geometry of Noncommutative Surfaces

A Riemannian geometry of noncommutative n-dimensional surfaces is developed as a first step towards the construction of a consistent noncommutative gravitational theory. Historically, as well, Riemannian geometry was recognized to be the underlying structure of Einstein's theory of general relativity and led to further developments of the latter. The notions of metric and connections on such noncommutative surfaces are introduced and it is shown that the connections are metric-compatible, giving rise to the corresponding Riemann curvature. The latter also satisfies the noncommutative analogue of the first and second Bianchi identities. As examples, noncommutative analogues of the sphere, torus and hyperboloid are studied in detail. The problem of covariance under appropriately defined general coordinate transformations is also discussed and commented on as compared with other treatments.Comment: 28 pages, some clarifications, examples and references added, version to appear in J. Math. Phy

Hydrodynamics in 1+1 dimensions with gravitational anomalies

The constraints imposed on hydrodynamics by the structure of gauge and gravitational anomalies are studied in two dimensions. By explicit integration of the consistent gravitational anomaly, we derive the equilibrium partition function at second derivative order. This partition function is then used to compute the parity-violating part of the covariant energy-momentum tensor and the transport coefficients.Comment: 9 pages, JHEP format.v2; added comments and references, matching published versio

Relating harmonic and projective descriptions of N=2 nonlinear sigma models

Recent papers have established the relationship between projective superspace and a complexified version of harmonic superspace. We extend this construction to the case of general nonlinear sigma models in both frameworks. Using an analogy with Hamiltonian mechanics, we demonstrate how the Hamiltonian structure of the harmonic action and the symplectic structure of the projective action naturally arise from a single unifying action on a complexified version of harmonic superspace. This links the harmonic and projective descriptions of hyperkahler target spaces. For the two examples of Taub-NUT and Eguchi-Hanson, we show how to derive the projective superspace solutions from the harmonic superspace solutions.Comment: 25 pages; v3: typo fixed in eq (1.36

An Introduction to T-Duality in String Theory

In these lectures a general introduction to T-duality is given. In the abelian case the approaches of Buscher, and Ro\u{c}ek and Verlinde are reviewed. Buscher's prescription for the dilaton transformation is recovered from a careful definition of the gauge integration measure. It is also shown how duality can be understood as a quite simple canonical transformation. Some aspects of non-abelian duality are also discussed, in particular what is known on relation to canonical transformations. Some implications of the existence of duality on the cosmological constant and the definition of distance in String Theory are also suggested.Comment: Latex file (1 figure), dina4p macro inserte

An effective theory of accelerated expansion

We work out an effective theory of accelerated expansion to describe general phenomena of inflation and acceleration (dark energy) in the Universe. Our aim is to determine from theoretical grounds, in a physically-motivated and model independent way, which and how many (free) parameters are needed to broadly capture the physics of a theory describing cosmic acceleration. Our goal is to make as much as possible transparent the physical interpretation of the parameters describing the expansion. We show that, at leading order, there are five independent parameters, of which one can be constrained via general relativity tests. The other four parameters need to be determined by observing and measuring the cosmic expansion rate only, H(z). Therefore we suggest that future cosmology surveys focus on obtaining an accurate as possible measurement of $H(z)$ to constrain the nature of accelerated expansion (dark energy and/or inflation).Comment: In press; minor changes, results unchange