### Abstract

We construct L-theory with complex coefficients from the geometry of 1|2-dimensional perturbative mechanics. Methods of perturbative quantization lead to wrong-way maps that we identify with those coming from the MSO orientation of L-theory tensored with the complex numbers. In particular, the total volume of a space of 1|2-dimensional vacua reads off the signature of a 4k-dimensional oriented manifold.

Original language | English (US) |
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Pages (from-to) | 109-129 |

Number of pages | 21 |

Journal | Letters in Mathematical Physics |

Volume | 106 |

Issue number | 1 |

DOIs | |

State | Published - Jan 1 2016 |

### Fingerprint

### Keywords

- algebraic topology of manifolds
- cohomological methods
- generalized (extraordinary) homology and cohomology theories
- quantization in field theory
- supersymmetric field theories

### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics

### Cite this

**Perturbative N = 2 Supersymmetric Quantum Mechanics and L-Theory with Complex Coefficients.** / Berwick Evans, Daniel.

Research output: Contribution to journal › Article

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TY - JOUR

T1 - Perturbative N = 2 Supersymmetric Quantum Mechanics and L-Theory with Complex Coefficients

AU - Berwick Evans, Daniel

PY - 2016/1/1

Y1 - 2016/1/1

N2 - We construct L-theory with complex coefficients from the geometry of 1|2-dimensional perturbative mechanics. Methods of perturbative quantization lead to wrong-way maps that we identify with those coming from the MSO orientation of L-theory tensored with the complex numbers. In particular, the total volume of a space of 1|2-dimensional vacua reads off the signature of a 4k-dimensional oriented manifold.

AB - We construct L-theory with complex coefficients from the geometry of 1|2-dimensional perturbative mechanics. Methods of perturbative quantization lead to wrong-way maps that we identify with those coming from the MSO orientation of L-theory tensored with the complex numbers. In particular, the total volume of a space of 1|2-dimensional vacua reads off the signature of a 4k-dimensional oriented manifold.

KW - algebraic topology of manifolds

KW - cohomological methods

KW - generalized (extraordinary) homology and cohomology theories

KW - quantization in field theory

KW - supersymmetric field theories

UR - http://www.scopus.com/inward/record.url?scp=84952630424&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84952630424&partnerID=8YFLogxK

U2 - 10.1007/s11005-015-0808-4

DO - 10.1007/s11005-015-0808-4

M3 - Article

AN - SCOPUS:84952630424

VL - 106

SP - 109

EP - 129

JO - Letters in Mathematical Physics

JF - Letters in Mathematical Physics

SN - 0377-9017

IS - 1

ER -