On Absence of 3-loop Divergence in N=4 Supergravity

We argue that N=4 supergravity is 3-loop UV finite because the relevant supersymmetric candidate counterterm is known to be SL(2, R)x SO(6) invariant, which violates the Noether-Gaillard-Zumino current conservation. Analogous arguments, based on the universality properties of groups of type E7, also apply to N=5,6,8 in 4,5,7 loops, respectively, since the 1/N BPS invariants break duality symmetry between Bianchi identities and quantum corrected vector field equations.Comment: 5 page

Stable fractal sums of pulses: the cylindrical case

A class of α-stable, 0\textlessα\textless2, processes is obtained as a sum of ’up-and-down’ pulses determined by an appropriate Poisson random measure. Processes are H-self-affine (also frequently called ’self-similar’) with H\textless1/α and have stationary increments. Their two-dimensional dependence structure resembles that of the fractional Brownian motion (for H\textless1/2), but their sample paths are highly irregular (nowhere bounded with probability 1). Generalizations using different shapes of pulses are also discussed

Supertwistors as Quarks of SU(2,2|4)

The GS superstring on AdS_5 x S^5 has a nonlinearly realized, spontaneously broken SU(2,2|4) symmetry. Here we introduce a two-dimensional model in which the unbroken SU(2,2|4) symmetry is linearly realized. The basic variables are supertwistors, which transform in the fundamental representation of this supergroup. The quantization of this supertwistor model leads to the complete oscillator construction of the unitary irreducible representations of the centrally extended SU(2,2|4). They include the states of d=4 SYM theory, massless and KK states of AdS_5 supergravity, and the descendants on AdS_5 of the standard massive string states, which form intermediate and long supermultiplets. We present examples of such multiplets and discuss possible states of solitonic and (p,q) strings.Comment: 12 pages, LaTeX, 1 EPS figur

Magic Supergravities, N= 8 and Black Hole Composites

We present explicit U-duality invariants for the R, C, Q, O$ (real, complex, quaternionic and octonionic) magic supergravities in four and five dimensions using complex forms with a reality condition. From these invariants we derive an explicit entropy function and corresponding stabilization equations which we use to exhibit stationary multi-center 1/2 BPS solutions of these N=2 d=4 theories, starting with the octonionic one with E_{7(-25)} duality symmetry. We generalize to stationary 1/8 BPS multicenter solutions of N=8, d=4 supergravity, using the consistent truncation to the quaternionic magic N=2 supergravity. We present a general solution of non-BPS attractor equations of the STU truncation of magic models. We finish with a discussion of the BPS-non-BPS relations and attractors in N=2 versus N= 5, 6, 8.Comment: 33 pages, references added plus brief outline at end of introductio

N=8 Supergravity on the Light Cone

We construct the generating functional for the light-cone superfield amplitudes in a chiral momentum superspace. It generates the n-point particle amplitudes which on shell are equivalent to the covariant ones. Based on the action depending on unconstrained light-cone chiral scalar superfield, this functional provides a regular d=4 QFT path integral derivation of the Nair-type amplitude constructions. By performing a Fourier transform into the light-cone chiral coordinate superspace we find that the quantum corrections to the superfield amplitudes with n legs are non-local in transverse directions for the diagrams with the number of loops smaller than n(n-1)/2 +1. This suggests the reason why UV infinities, which are proportional to local vertices, cannot appear at least before 7 loops in the light-cone supergraph computations. By combining the E7 symmetry with the supersymmetric recursion relations we argue that the light-cone supergraphs predict all loop finiteness of d=4 N=8 supergravity.Comment: 38

Volume Stabilization and the Origin of the Inflaton Shift Symmetry in String Theory

The main problem of inflation in string theory is finding the models with a flat potential, consistent with stabilization of the volume of the compactified space. This can be achieved in the theories where the potential has (an approximate) shift symmetry in the inflaton direction. We will identify a class of models where the shift symmetry uniquely follows from the underlying mathematical structure of the theory. It is related to the symmetry properties of the corresponding coset space and the period matrix of special geometry, which shows how the gauge coupling depends on the volume and the position of the branes. In particular, for type IIB string theory on K3xT^2/Z with D3 or D7 moduli belonging to vector multiplets, the shift symmetry is a part of SO(2,2+n) symmetry of the coset space [SU(1,1)/ U(1)]x[SO(2,2+n)/(SO(2)x SO(2+n)]. The absence of a prepotential, specific for the stringy version of supergravity, plays a prominent role in this construction, which may provide a viable mechanism for the accelerated expansion and inflation in the early universe.Comment: 12 page

N=2 Extremal Black Holes

It is shown that extremal magnetic black hole solutions of N = 2 supergravity coupled to vector multiplets $X^\Lambda$ with a generic holomorphic prepotential $F(X^\Lambda)$ can be described as supersymmetric solitons which interpolate between maximally symmetric limiting solutions at spatial infinity and the horizon. A simple exact solution is found for the special case that the ratios of the $X^\Lambda$ are real, and it is seen that the logarithm of the conformal factor of the spatial metric equals the Kahler potential on the vector multiplet moduli space. Several examples are discussed in detail.Comment: 10 pages, minor correction