### Abstract

This paper, in a sense, completes a series of three papers. In the previous two [1],[2], we have explored the possibility of refining the K-theory partition function in type II string theories using elliptic cohomology. In the present paper, we make that more concrete by defining a fully quantized free field theory based on elliptic cohomology of 10-dimensional spacetime. Moreover, we describe a concrete scenario how this is related to compactification of F-theory on an elliptic curve leading to IIA and IIB theories. We propose an interpretation of the elliptic curve in the context of elliptic cohomology. We discuss the possibility of orbifolding of the elliptic curves and derive certain properties of F-theory. We propose a link of this to type IIB modularity, the structure of the topological lagrangian of M-theory, and Witten's index of loop space Dirac operators. The discussion suggests a S^{1}-lift of type IIB and an F-theoretic model for type I obtained by orbifolding that for type IIB.

Original language | English (US) |
---|---|

Pages (from-to) | 1041-1070 |

Number of pages | 30 |

Journal | Journal of High Energy Physics |

Issue number | 8 |

DOIs | |

State | Published - Aug 1 2005 |

### Fingerprint

### Keywords

- F-Theory
- M-Theory
- String Duality
- Superstrings and Heterotic Strings

### ASJC Scopus subject areas

- Nuclear and High Energy Physics

### Cite this

*Journal of High Energy Physics*, (8), 1041-1070. https://doi.org/10.1088/1126-6708/2005/08/038

**Type II string theory and modularity.** / Kriz, Igor; Sati, Hisham.

Research output: Contribution to journal › Article

*Journal of High Energy Physics*, no. 8, pp. 1041-1070. https://doi.org/10.1088/1126-6708/2005/08/038

}

TY - JOUR

T1 - Type II string theory and modularity

AU - Kriz, Igor

AU - Sati, Hisham

PY - 2005/8/1

Y1 - 2005/8/1

N2 - This paper, in a sense, completes a series of three papers. In the previous two [1],[2], we have explored the possibility of refining the K-theory partition function in type II string theories using elliptic cohomology. In the present paper, we make that more concrete by defining a fully quantized free field theory based on elliptic cohomology of 10-dimensional spacetime. Moreover, we describe a concrete scenario how this is related to compactification of F-theory on an elliptic curve leading to IIA and IIB theories. We propose an interpretation of the elliptic curve in the context of elliptic cohomology. We discuss the possibility of orbifolding of the elliptic curves and derive certain properties of F-theory. We propose a link of this to type IIB modularity, the structure of the topological lagrangian of M-theory, and Witten's index of loop space Dirac operators. The discussion suggests a S1-lift of type IIB and an F-theoretic model for type I obtained by orbifolding that for type IIB.

AB - This paper, in a sense, completes a series of three papers. In the previous two [1],[2], we have explored the possibility of refining the K-theory partition function in type II string theories using elliptic cohomology. In the present paper, we make that more concrete by defining a fully quantized free field theory based on elliptic cohomology of 10-dimensional spacetime. Moreover, we describe a concrete scenario how this is related to compactification of F-theory on an elliptic curve leading to IIA and IIB theories. We propose an interpretation of the elliptic curve in the context of elliptic cohomology. We discuss the possibility of orbifolding of the elliptic curves and derive certain properties of F-theory. We propose a link of this to type IIB modularity, the structure of the topological lagrangian of M-theory, and Witten's index of loop space Dirac operators. The discussion suggests a S1-lift of type IIB and an F-theoretic model for type I obtained by orbifolding that for type IIB.

KW - F-Theory

KW - M-Theory

KW - String Duality

KW - Superstrings and Heterotic Strings

UR - http://www.scopus.com/inward/record.url?scp=24944495791&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=24944495791&partnerID=8YFLogxK

U2 - 10.1088/1126-6708/2005/08/038

DO - 10.1088/1126-6708/2005/08/038

M3 - Article

AN - SCOPUS:24944495791

SP - 1041

EP - 1070

JO - Journal of High Energy Physics

JF - Journal of High Energy Physics

SN - 1126-6708

IS - 8

ER -