On R**4 threshold corrections in IIb string theory and (p, q) string instantons

Kiritsis, Elias; Pioline, Boris

doi:10.1016/S0550-3213(97)00645-7

On R**4 threshold corrections in IIb string theory and (p, q) string instantons

Elias Kiritsis
(
- CERN
)
,
Boris Pioline
(
- CERN
)

Jul, 1997

22 pages

Published in:

Nucl.Phys.B 508 (1997) 509-534

e-Print:

hep-th/9707018 [hep-th]

DOI:

10.1016/S0550-3213(97)00645-7

Report number:

CERN-TH-97-146,
CPTH-S539-0697

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Abstract:

We obtain the exact non-perturbative thresholds of

R^4

terms in IIB string theory compactified to eight and seven dimensions. These thresholds are given by the perturbative tree-level and one-loop results together with the contribution of the D-instantons and of the

(p,q)

-string instantons. The invariance under U-duality is made manifest by rewriting the sum as a non-holomorphic modular function of the corresponding discrete U-duality group. In the eight-dimensional case, the threshold is the sum of a order-1 Eisenstein series for

SL(2,Z)

and a order-3/2 Eisenstein series for

SL(3,Z)

. The seven-dimensional result is given by the order-3/2 Eisenstein series for

SL(5,Z)

. We also conjecture formulae for the non-perturbative thresholds in lower dimensional compactifications and discuss the relation with M-theory.

Note:

24 pages, Latex, eqs. (3.8) and (4.2) corrected Report-no: CERN-TH/97-146, CPTH-S539.0697 Journal-ref: Nucl.Phys. B508 (1997) 509-534

11.25.-w
11.25.Sq
11.30.Pb
Gravitational corrections
Non-perturbativeeffects
D-instantons
( p , q )-strings
U -duality
Eisenstein series
( p, q)-strings

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