# Dimensional Duality

## Abstract

We show that string theory on a compact negatively curved manifold, preserving a U(1)b1 winding symmetry, grows at least b1 new effective dimensions as the space shrinks. The winding currents yield a ''D-dual'' description of a Riemann surface of genus h in terms of its 2h dimensional Jacobian torus, perturbed by a closed string tachyon arising as a potential energy term in the worldsheet sigma model. D-branes on such negatively curved manifolds also reveal this structure, with a classical moduli space consisting of a b{sub 1}-torus. In particular, we present an AdS/CFT system which offers a non-perturbative formulation of such supercritical backgrounds. Finally, we discuss generalizations of this new string duality.

- Authors:

- Publication Date:

- Research Org.:
- Stanford Linear Accelerator Center (SLAC)

- Sponsoring Org.:
- USDOE

- OSTI Identifier:
- 907709

- Report Number(s):
- SLAC-PUB-12439

Journal ID: ISSN 0031-9007; PRLTAO; arXiv:0705.0550; TRN: US0703360

- DOE Contract Number:
- AC02-76SF00515

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physical Review Letters

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; DIMENSIONS; DUALITY; POTENTIAL ENERGY; RIEMANN SHEET; SIGMA MODEL; SYMMETRY; TACHYONS; Theory-HEP,HEPTH

### Citation Formats

```
Green, Daniel, /SLAC /Stanford U., Phys. Dept., Lawrence, Albion, /Brandeis U., McGreevy, John, /MIT, LNS, Morrison, David R., /Duke U., CGTP /UC, Santa Barbara, Silverstein,
Eva, and /SLAC /Stanford U., Phys. Dept.
```*Dimensional Duality*. United States: N. p., 2007.
Web. doi:10.1103/PhysRevD.76.066004.

```
Green, Daniel, /SLAC /Stanford U., Phys. Dept., Lawrence, Albion, /Brandeis U., McGreevy, John, /MIT, LNS, Morrison, David R., /Duke U., CGTP /UC, Santa Barbara, Silverstein,
Eva, & /SLAC /Stanford U., Phys. Dept.
```*Dimensional Duality*. United States. doi:10.1103/PhysRevD.76.066004.

```
Green, Daniel, /SLAC /Stanford U., Phys. Dept., Lawrence, Albion, /Brandeis U., McGreevy, John, /MIT, LNS, Morrison, David R., /Duke U., CGTP /UC, Santa Barbara, Silverstein,
Eva, and /SLAC /Stanford U., Phys. Dept. Fri .
"Dimensional Duality". United States.
doi:10.1103/PhysRevD.76.066004. https://www.osti.gov/servlets/purl/907709.
```

```
@article{osti_907709,
```

title = {Dimensional Duality},

author = {Green, Daniel and /SLAC /Stanford U., Phys. Dept. and Lawrence, Albion and /Brandeis U. and McGreevy, John and /MIT, LNS and Morrison, David R. and /Duke U., CGTP /UC, Santa Barbara and Silverstein,
Eva and /SLAC /Stanford U., Phys. Dept.},

abstractNote = {We show that string theory on a compact negatively curved manifold, preserving a U(1)b1 winding symmetry, grows at least b1 new effective dimensions as the space shrinks. The winding currents yield a ''D-dual'' description of a Riemann surface of genus h in terms of its 2h dimensional Jacobian torus, perturbed by a closed string tachyon arising as a potential energy term in the worldsheet sigma model. D-branes on such negatively curved manifolds also reveal this structure, with a classical moduli space consisting of a b{sub 1}-torus. In particular, we present an AdS/CFT system which offers a non-perturbative formulation of such supercritical backgrounds. Finally, we discuss generalizations of this new string duality.},

doi = {10.1103/PhysRevD.76.066004},

journal = {Physical Review Letters},

number = ,

volume = ,

place = {United States},

year = {Fri May 18 00:00:00 EDT 2007},

month = {Fri May 18 00:00:00 EDT 2007}

}

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