Minimal unitary representations from supersymmetry

We compute the supersymmetry constraints on the R^4 type corrections in maximal supergravity in dimension 8, 6, 4 and 3, and determine the tensorial differential equations satisfied by the function of the scalar fields multiplying the R^4 term in the corresponding invariants. The second order derivative of this function restricted to the Joseph ideal vanishes in dimension lower than six. These results are extended to the d^4 R^4 and the d^6 R^4 corrections, based on the harmonic superspace construction of these invariants in the linearised approximation. We discuss the solutions of these differential equations and analysis the consequences on the non-perturbative type II low energy string theory effective action.Comment: 84 pages, Corrected version for publication in JHEP, additional comment on d^6 R^4 in four dimension

The cohomology of superspace, pure spinors and invariant integrals

The superform construction of supersymmetric invariants, which consists of integrating the top component of a closed superform over spacetime, is reviewed. The cohomological methods necessary for the analysis of closed superforms are discussed and some further theoretical developments presented. The method is applied to higher-order corrections in heterotic string theory up to \a'^3. Some partial results on $N=2,d=10$ and $N=1,d=11$ are also given.Comment: 24 pages. Minor changes; added reference

4-point effective actions in open and closed superstring theory

Recently the effective action for the 4-point functions in abelian open superstring theory has been derived, giving an explicit construction of the bosonic and fermionic terms of this infinite $\alpha'$ series. In the present work we generalize this result to the nonabelian case. We test our result, at ${\alpha'}^3$ and ${\alpha'}^4$ order, with several existing versions for these terms, finding agreement in most of the cases. We also apply these ideas to derive the effective action for the 4-point functions of the NS-NS sector of closed superstring theory, to all order in $\alpha'$.Comment: 26 pages, 1 figure. To appear in JHE

Abelian M5-brane on S6S^6

We study the abelian M5 brane on $S^6$. From the spectrum we extract a series expansion for the heat kernel. In particular we determine the normalization for the coefficient $a$ in the M5 brane conformal anomaly. When we compare our result with what one gets by computing the Hadamard-Minakshisundaram-DeWitt-Seeley coefficients from local curvature invariants on $S^6$, we first find a mismatch of one unit. This mismatch is due to an overcounting of one zero mode. After subtracting this contribution, we finally find agreement. We perform dimensional reduction along a singular circle fiber to five dimensions where we find the conformal anomaly vanishes.Comment: 40 page