# Duality groups, automorphic forms, and higher derivative corrections

## Abstract

We study the higher derivative corrections that occur in type II superstring theories in ten dimensions or less. Assuming invariance under a discrete duality group G(Z) we show that the generic functions of the scalar fields that occur can be identified with automorphic forms. We then give a systematic method to construct automorphic forms from a given group G(Z) together with a chosen subgroup H and a linear representation of G(Z). This construction is based on the theory of nonlinear realizations and we find that the automorphic forms contain the weights of G. We also carry out the dimensional reduction of the generic higher derivative corrections of the IIB theory to three dimensions and find that the weights of E{sub 8} occur generalizing previous results of the authors on M theory. Since the automorphic forms of this theory contain the weights of E{sub 8} we can interpret the occurrence of weights in the dimensional reduction as evidence for an underlying U-duality symmetry.

- Authors:

- Department of Mathematics, King's College, London WC2R 2LS (United Kingdom)

- Publication Date:

- OSTI Identifier:
- 21020214

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physical Review. D, Particles Fields; Journal Volume: 75; Journal Issue: 6; Other Information: DOI: 10.1103/PhysRevD.75.066002; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; CORRECTIONS; DUALITY; M-THEORY; MANY-DIMENSIONAL CALCULATIONS; NONLINEAR PROBLEMS; QUANTUM FIELD THEORY; SCALAR FIELDS; SUPERSTRING MODELS; SYMMETRY

### Citation Formats

```
Lambert, Neil, and West, Peter.
```*Duality groups, automorphic forms, and higher derivative corrections*. United States: N. p., 2007.
Web. doi:10.1103/PHYSREVD.75.066002.

```
Lambert, Neil, & West, Peter.
```*Duality groups, automorphic forms, and higher derivative corrections*. United States. doi:10.1103/PHYSREVD.75.066002.

```
Lambert, Neil, and West, Peter. Thu .
"Duality groups, automorphic forms, and higher derivative corrections". United States.
doi:10.1103/PHYSREVD.75.066002.
```

```
@article{osti_21020214,
```

title = {Duality groups, automorphic forms, and higher derivative corrections},

author = {Lambert, Neil and West, Peter},

abstractNote = {We study the higher derivative corrections that occur in type II superstring theories in ten dimensions or less. Assuming invariance under a discrete duality group G(Z) we show that the generic functions of the scalar fields that occur can be identified with automorphic forms. We then give a systematic method to construct automorphic forms from a given group G(Z) together with a chosen subgroup H and a linear representation of G(Z). This construction is based on the theory of nonlinear realizations and we find that the automorphic forms contain the weights of G. We also carry out the dimensional reduction of the generic higher derivative corrections of the IIB theory to three dimensions and find that the weights of E{sub 8} occur generalizing previous results of the authors on M theory. Since the automorphic forms of this theory contain the weights of E{sub 8} we can interpret the occurrence of weights in the dimensional reduction as evidence for an underlying U-duality symmetry.},

doi = {10.1103/PHYSREVD.75.066002},

journal = {Physical Review. D, Particles Fields},

number = 6,

volume = 75,

place = {United States},

year = {Thu Mar 15 00:00:00 EDT 2007},

month = {Thu Mar 15 00:00:00 EDT 2007}

}