Localizations on Moduli Spaces and Free Field Realizations of Feynman Rules

Jian Zhou

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Localizations on Moduli Spaces and Free Field Realizations of Feynman Rules

Jian Zhou

Algebraic Geometry · Submitted 18 Oct 2003

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The authors' main claim We prove Iqbal's conjecture on the relationship between the free energy of closed string theory in local toric geometry and the Wess-Zumino-Witten model.

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We prove Iqbal's conjecture on the relationship between the free energy of closed string theory in local toric geometry and the Wess-Zumino-Witten model. This is achieved by first reformulating the calculations of the free energy by localization techniques in terms of suitable Feynman rule, then exploiting a realization of the Feynman rule by free bosons. We also use a formula of Hodge integrals conjectured by the author and proved jointly with Chiu-Chu Melissa Liu and Kefeng Liu.

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#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We prove Iqbal's conjecture on the relationship between the free energy of closed string theory in local toric geometry and the Wess-Zumino-Witten model.	result 0.73	0.92	0.92	asserted 1.00
s1	This is achieved by first reformulating the calculations of the free energy by localization techniques in terms of suitable Feynman rule, then exploiting a realization of the Feynman rule by free bosons.	method 1.00	0.92	0.09	asserted 1.00
s2	We also use a formula of Hodge integrals conjectured by the author and proved jointly with Chiu-Chu Melissa Liu and Kefeng Liu.	method 0.75	0.59	0.04	asserted 0.96

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Original abstract

We prove Iqbal's conjecture on the relationship between the free energy of closed string theory in local toric geometry and the Wess-Zumino-Witten model. This is achieved by first reformulating the calculations of the free energy by localization techniques in terms of suitable Feynman rule, then exploiting a realization of the Feynman rule by free bosons. We also use a formula of Hodge integrals conjectured by the author and proved jointly with Chiu-Chu Melissa Liu and Kefeng Liu.

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4 arXiv papers cite this in 7 sentences

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The instanton part of the free energy of $κ_^2$ is F^κ_^2 = ∑_g ≥0 λ^2g-2 ∑_d > 0 K^g_d(κ_^2) ·t^d, and the topological partition function of the local $^2$ geometry is defined by [equation] It can be explicitly computed [ref] by Chern-Simons invariants of Hopf link: [equation] For a fixed $d≥1$, denote the coefficient of $t^d$ in $Z^κ_^2$ by $(d)$, and denote by $F(d)$ the coefficient of $t^d$ in $F^κ_^2$, i.e., we have Z^κ_^2 = 1+ ∑_d ≥1 (d) t^d, F^κ_^2 = ∑_d ≥1 F(d) t^d.

Gopakumar-Vafa BPS invariants, Hilbert schemes and quasimodular forms. I · A formula for the free energy $F^κ_^2$ · 0.86
On the other hand, one can compute the Gromov-Witten invariants of $^2/_n ×$ by localization using the method of [ref] , or use the theory of topological vertex [ref] .

Crepant resolution conjecture in all genera for type A singularities · Introduction · 0.99

Cites it as background 1 paper

Some progress toward the calculation of Gromov-Witten invariants is present in physical approaches [ref] and in mathematical treatments [ref] .

String Partition Functions, Hilbert Schemes, and Affine Lie Algebra Representations on Homology Groups · Introduction · 0.95

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