Supergravity limit of genus two modular graph functions in the worldline formalism

We consider the contributions upto the $D^{10} \mathcal{R}^4$ terms in the low momentum expansion of the two loop four graviton amplitude in maximal supergravity that arise in the field theory limit of genus two modular graph functions that result from the low momentum expansion of the four graviton amplitude in toroidally compactified type II string theory, using the worldline formalism of the first quantized superparticle. The expression for the two loop supergravity amplitude in the worldline formalism allows us to obtain contributions from the individual graphs, unlike the expression for the same amplitude obtained using unitarity cuts which only gives the total contribution from the sum of all the graphs. Our two loop analysis is field theoretic, and does not make explicit use of the genus two string amplitude.Comment: 19 pages, 5 figures, LaTeX, v2: supersedes published versio

Low momentum expansion of one loop amplitudes in heterotic string theory

We consider the low momentum expansion of the four graviton and the two graviton--two gluon amplitudes in heterotic string theory at one loop in ten dimensions, and analyze contributions upto the D^2 R^4 interaction from the four graviton amplitude, and the D^4 R^2 F^2 interaction from the two graviton--two gluon amplitude. The calculations are performed by obtaining equations for the relevant modular graph functions that arise in the modular invariant integrals, and involve amalgamating techniques used in the type II theory and the calculation of the elliptic genus in the heterotic theory.Comment: 67 pages, LaTeX, 14 figure

Higher Derivative Corrections in Holographic QCD

We consider the effect of the R^4 term in type IIA string theory on the supergravity background dual to N_c D4 branes compactified on a circle with supersymmetry breaking boundary conditions. We study the dynamics of D8 branes in this perturbed geometry in the probe approximation. This leads to an analysis of higher derivative corrections in holographic QCD beyond the supergravity approximation. We make a rough estimate of the corrections to the masses of some of the lightest (axial) vector mesons. The corrections are suppressed by a factor of (g_{YM}^2 N_c)^{-3} compared to their supergravity values. We find that the masses of these mesons increase from their supergravity values.Comment: 24 pages, LaTe

Constraining the D3-brane effective action

We consider higher derivative corrections of the type D^{2k} R^2 in the effective action of the D3-brane with trivial normal bundle. Based on the perturbative disc and annulus amplitudes, and constraints of supersymmetry and duality, we argue that these interactions are protected, at least for small values of k. Their coefficient functions receive only a finite number of perturbative contributions, and non-perturbative contributions from D-instantons. We propose expressions for these modular forms for low values of k.Comment: 22 pages, LaTe