On a Dual Heterotic Kodaira-Spencer Theory
Abstract
We consider a dual version of heterotic Kodaira-Spencer theory on a Calabi-Yau three-fold X with background fluxes, related to the type I BCOV theory of Costello-Li. We implement the Green-Schwarz mechanism of Costello-Li, where the Beltrami differential plays the role of the Green-Schwarz field. On a compact Calabi-Yau three-fold with background gauge fluxes F, where tr(F2) is trivial in cohomology, retaining gauge anomalies only and leaving gravitational anomalies to future work, we incorporate the Costello-Li Green-Schwarz mechanism into the classical deformation complex. This gives a theory governed by a nilpotent operator D̅ on Q=T1,0X⊕End(V)⊕ T*1,0X, whose extension maps carry holomorphic derivatives, so that (Q,D̅) is not a holomorphic bundle. Using diagonal ∂̅†-gauge, the one-loop gauge anomaly cancels, assuming that the extension maps of D̅ do not modify it, which we argue is plausible. Introducing an auxiliary (0,2)-form, we construct a cubic interacting theory whose gauge symmetries are governed by an L3 algebra. On compact Calabi-Yau three-folds, and for sufficiently small fields, we show that the equation of motion is equivalent to the Maurer-Cartan equation, together with a divergence-free constraint on the Beltrami differential. Finally we trivialise D̅ locally to the Dolbeault operator. The (non-tensorial) transition maps glue into a quasi-holomorphic extension sheaf 𝒬̃, for which we prove a Dolbeault theorem, H0,qD̅(Q)≅check Hq(𝒬̃).
Related
BibTeX
@misc{mangamuri2026dual,
title = {{On a Dual Heterotic Kodaira-Spencer Theory}},
author = {Siddhartha Mangamuri and Eirik Eik Svanes and Anuthi Tiwary},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.07178},
eprint = {2611.07178},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.07178},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - On a Dual Heterotic Kodaira-Spencer Theory
AU - Siddhartha Mangamuri
AU - Eirik Eik Svanes
AU - Anuthi Tiwary
PY - 2026
DA - 2026/11/04
PB - arXiv
DO - 10.48550/arxiv.2611.07178
UR - https://arxiv.org/abs/2611.07178
AB - We consider a dual version of heterotic Kodaira-Spencer theory on a Calabi-Yau three-fold X with background fluxes, related to the type I BCOV theory of Costello-Li. We implement the Green-Schwarz mechanism of Costello-Li, where the Beltrami differential plays the role of the Green-Schwarz field. On a compact Calabi-Yau three-fold with background gauge fluxes F, where tr(F^2) is trivial in cohomology, retaining gauge anomalies only and leaving gravitational anomalies to future work, we incorporate the Costello-Li Green-Schwarz mechanism into the classical deformation complex. This gives a theory governed by a nilpotent operator D̅ on Q=T^1,0X⊕End(V)⊕ T^*1,0X, whose extension maps carry holomorphic derivatives, so that (Q,D̅) is not a holomorphic bundle. Using diagonal ∂̅^†-gauge, the one-loop gauge anomaly cancels, assuming that the extension maps of D̅ do not modify it, which we argue is plausible. Introducing an auxiliary (0,2)-form, we construct a cubic interacting theory whose gauge symmetries are governed by an L_3 algebra. On compact Calabi-Yau three-folds, and for sufficiently small fields, we show that the equation of motion is equivalent to the Maurer-Cartan equation, together with a divergence-free constraint on the Beltrami differential. Finally we trivialise D̅ locally to the Dolbeault operator. The (non-tensorial) transition maps glue into a quasi-holomorphic extension sheaf 𝒬̃, for which we prove a Dolbeault theorem, H^0,q_D̅(Q)≅check H^q(𝒬̃).
ER -