8 research outputs found
Higher derivative type II string effective actions, automorphic forms and E11
By dimensionally reducing the ten-dimensional higher derivative type IIA
string theory effective action we place constraints on the automorphic forms
that appear in the effective action in lower dimensions. We propose a number of
properties of such automorphic forms and consider the prospects that E11 can
play a role in the formulation of the higher derivative string theory effective
action.Comment: 34 page
Supersymmetry constraints on the R^4 multiplet in type IIB on T^2
We consider a class of eight derivative interactions in the effective action
of type IIB string theory compactified on T^2. These 1/2 BPS interactions have
moduli dependent couplings. We impose the constraints of supersymmetry to show
that each of these couplings satisfy a first order differential equation on
moduli space which relate it to other couplings in the same supermuliplet.
These equations can be iterated to give second order differential equations for
the various couplings. The couplings which only depend on the SO(2)\SL(2,R)
moduli satisfy Laplace equation on moduli space, and are given by modular forms
of SL(2,Z). On the other hand, the ones that only depend on the SO(3)\SL(3,R)
moduli satisfy Poisson equation on moduli space, where the source terms are
given by other couplings in the same supermultiplet. The couplings of the
interactions which are charged under SU(2) are not automorphic forms of
SL(3,Z). Among the interactions we consider, the R^4 coupling depends on all
the moduli.Comment: 89 pages, LaTe
Constraints on Automorphic Forms of Higher Derivative Terms from Compactification
By dimensionally reducing the higher derivative corrections of
ten-dimensional IIB theory on a torus we deduce constraints on the E_{n+1}
automorphic forms that occur in d=10-n dimensions. In particular we argue that
these automorphic forms involve the representation of E_{n+1} with fundamental
weight \lambda^{n+1}, which is also the representation to which the string
charges in d dimensions belong. We also consider a similar calculation for the
reduction of higher derivative terms in eleven-dimensional M-theory.Comment: Minor corrections, to appear in JHE
Eisenstein series for infinite-dimensional U-duality groups
We consider Eisenstein series appearing as coefficients of curvature
corrections in the low-energy expansion of type II string theory four-graviton
scattering amplitudes. We define these Eisenstein series over all groups in the
E_n series of string duality groups, and in particular for the
infinite-dimensional Kac-Moody groups E9, E10 and E11. We show that,
remarkably, the so-called constant term of Kac-Moody-Eisenstein series contains
only a finite number of terms for particular choices of a parameter appearing
in the definition of the series. This resonates with the idea that the constant
term of the Eisenstein series encodes perturbative string corrections in
BPS-protected sectors allowing only a finite number of corrections. We underpin
our findings with an extensive discussion of physical degeneration limits in
D<3 space-time dimensions.Comment: 69 pages. v2: Added references and small additions, to be published
in JHE