The low energy expansion of the one-loop type II superstring amplitude

The one-loop four-graviton amplitude in either of the type II superstring theories is expanded in powers of the external momenta up to and including terms of order s^4 log s R^4, where R^4 denotes a specific contraction of four linearized Weyl tensors and s is a Mandelstam invariant. Terms in this series are obtained by integrating powers of the two-dimensional scalar field theory propagator over the toroidal world-sheet as well as the moduli of the torus. The values of these coefficients match expectations based on duality relations between string theory and eleven-dimensional supergravity.Comment: harvmac (b), 25 pages, 3 eps figures. v2: Factors of 2 corrected. Conclusion unchange

Supersymmetry Constraints on Type IIB Supergravity

Supersymmetry is used to derive conditions on higher derivative terms in the effective action of type IIB supergravity. Using these conditions, we are able to prove earlier conjectures that certain modular invariant interactions of order alpha' **3 relative to the Einstein-Hilbert term are proportional to eigenfunctions of the Laplace operator on the fundamental domain of SL(2,Z). We also discuss how these arguments generalize to terms of higher order in alpha', as well as to compactifications of supergravity.Comment: 31 pages, harvmac (b); minor correction

Momentum Analyticity and Finiteness of the 1-Loop Superstring Amplitude

The Type II Superstring amplitude to 1-loop order is given by an integral of $\vartheta$-functions over the moduli space of tori, which diverges for real momenta. We construct the analytic continuation which renders this amplitude well defined and finite, and we find the expected poles and cuts in the complex momentum plane.Comment: 10pp, /UCLA/93/TEP/

D-instanton partition functions

Duality arguments are used to determine D-instanton contributions to certain effective interaction terms of type II supergravity theories in various dimensions. This leads to exact expressions for the partition functions of the finite N D-instanton matrix model in d=4 and 6 dimensions that generalize our previous expression for the case d=10. These results are consistent with the fact that the Witten index of the T-dual D-particle process should only be non-vanishing for d=10.Comment: 20 pages, harvmac, typos corrected, reference adde

Internal Space for the Noncommutative Geometry Standard Model and Strings

In this paper I discuss connections between the noncommutative geometry approach to the standard model on one side, and the internal space coming from strings on the other. The standard model in noncommutative geometry is described via the spectral action. I argue that an internal noncommutative manifold compactified at the renormalization scale, could give rise to the almost commutative geometry required by the spectral action. I then speculate how this could arise from the noncommutative geometry given by the vertex operators of a string theory.Comment: 1+22 pages. More typos and misprints correcte

Combinatorics of Boundaries in String Theory

We investigate the possibility that stringy nonperturbative effects appear as holes in the world-sheet. We focus on the case of Dirichlet string theory, which we argue should be formulated differently than in previous work, and we find that the effects of boundaries are naturally weighted by $e^{-O(1/g_{\rm st})}$.Comment: 12 pages, 2 figures, LaTe

Maximum temperature for an Ideal Gas of U^(1)\hat U(1) Kac-Moody Fermions

A lagrangian for gauge fields coupled to fermions with the Kac-Moody group as its gauge group yields, for the pure fermions sector, an ideal gas of Kac-Moody fermions. The canonical partition function for the $\hat U(1)$ case is shown to have a maximum temperature $kT_{M} = |\lambda| /\pi$, where $\lambda$ is the coupling of the super charge operator $G_0$ to the fermions. This result is similar to the case of strings but unlike strings the result is obtained from a well-defined lagrangian.Comment: Needs subeqnarray.sty; To be published in Phys. Rev. D, Dec 15, 1995. Some typographical errors have been corrected in the revised versio

Large Radius Hagedorn Regime in String Gas Cosmology

We calculate the equation of state of a gas of strings at high density in a large toroidal universe, and use it to determine the cosmological evolution of background metric and dilaton fields in the entire large radius Hagedorn regime, (ln S)^{1/d} << R << S^{1/d} (with S the total entropy). The pressure in this regime is not vanishing but of O(1), while the equation of state is proportional to volume, which makes our solutions significantly different from previously published approximate solutions. For example, we are able to calculate the duration of the high-density "Hagedorn" phase, which increases exponentially with increasing entropy, S. We go on to discuss the difficulties of the scenario, quantifying the problems of establishing thermal equilibrium and producing a large but not too weakly-coupled universe.Comment: 12 pages, 4 figures, more details presented in string thermodynamics section, to be published in Physical Review

Primordial black holes as a tool for constraining non-Gaussianity

Primordial Black Holes (PBH's) can form in the early Universe from the collapse of large density fluctuations. Tight observational limits on their abundance constrain the amplitude of the primordial fluctuations on very small scales which can not otherwise be constrained, with PBH's only forming from the extremely rare large fluctuations. The number of PBH's formed is therefore sensitive to small changes in the shape of the tail of the fluctuation distribution, which itself depends on the amount of non-Gaussianity present. We study, for the first time, how quadratic and cubic local non-Gaussianity of arbitrary size (parameterised by f_nl and g_nl respectively) affects the PBH abundance and the resulting constraints on the amplitude of the fluctuations on very small scales. Intriguingly we find that even non-linearity parameters of order unity have a significant impact on the PBH abundance. The sign of the non-Gaussianity is particularly important, with the constraint on the allowed fluctuation amplitude tightening by an order of magnitude as f_nl changes from just -0.5 to 0.5. We find that if PBH's are observed in the future, then regardless of the amplitude of the fluctuations, non-negligible negative f_nl would be ruled out. Finally we show that g_nl can have an even larger effect on the number of PBH's formed than f_nl.Comment: 9 pages, 5 figures, v2: version to appear in Phys. Rev. D with minor changes, v3: typos corrected (including factor of 1/2 in erfc prefactor), no changes to result