Elliptic Genera and Quantum Field Theory

It is shown that in elliptic cohomology — as recently formulated in the mathematical literature — the supercharge of the supersymmetric nonlinear signa model plays a role similar to the role of the Dirac operator inK-theory. This leads to several insights concerning both elliptic cohomology and string theory. Some of the relevant calculations have been done previously by Schellekens and Warner in a different context.

FIELD THEORETICAL MODEL: SIGMA
NONLINEAR
SUPERSYMMETRY: TRANSFORMATION
INVARIANCE: CPT
Dirac equation
MATHEMATICAL METHODS: GEOMETRICAL

References(9)

Figures(0)

The Index of elliptic operators. 1

M.F. Atiyah
(
- Oxford U. and
- UC, Berkeley
)
,
I.M. Singer
(
- Oxford U. and
- UC, Berkeley
)

- Annals Math. 87 (1968) 484-530
•
DOI:
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- Annals Math. 87 586

The Index of elliptic operators. 2.

M.F. Atiyah
(
- Oxford U.
)
,
G.B. Segal
(
- Oxford U.
)

- Annals Math. 87 (1968) 531-545
•
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Strings on Orbifolds

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•
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The Index of elliptic operators. 4

M.F. Atiyah
(
- Princeton, Inst. Advanced Study
)
,
I.M. Singer
(
- MIT, LNS
)

- Annals Math. 93 (1971) 119-138
•
DOI:
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Regularized, Continuum {Yang-Mills} Process and {Feynman-Kac} Functional Integral

M. Asorey
(
- Paris U., VI-VII
)
,
P.K. Mitter
(
- Paris U., VI-VII
)

- Commun.Math.Phys. 80 (1981) 43
•
DOI:
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Continuum Regularization of {QCD}

Z. Bern
(
- LBL, Berkeley and
- UC, Berkeley
)
,
M.B. Halpern
(
- LBL, Berkeley and
- UC, Berkeley
)
,
L. Sadun
(
- UC, Berkeley
)
,
Clifford Henry Taubes
(
- UC, Berkeley, Math. Dept.
)

- Phys.Lett.B 165 (1985) 151,
- IN *DAMGAARD, P.H. (ED.), HUEFFEL, H. (ED.): STOCHASTIC QUANTIZATION*, 310-315. (PHYS. LETT. B165 (1985) 151-156) AND LAWRENCE BERKELEY LAB. - LBL-19900 (85,REC.OCT.) 11 P. (SEE BOOK INDEX)
•
DOI:
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Nonabelian Bosonization in Two-Dimensions

Edward Witten
(
- Princeton U.
)

- Commun.Math.Phys. 92 (1984) 455-472,
•
DOI:
- 10.1007/BF01215276