What does this research mean for the field?

The perturbative path integral of Chern-Simons theory in the BV formalism can be used to construct a 'global partition function' on the moduli space of flat connections, yielding a metric-independent 3-manifold invariant. Novelty: ClaimNovelty.NOVEL_FINDING. Consensus alignment: ConsensusAlignment.NEUTRAL.

What question did this study set out to answer?

To globalize the perturbative path integral of Chern–Simons theory over the moduli space of flat connections within the Batalin–Vilkovisky (BV) framework.

August 30, 2026Communications in Mathematical PhysicsOpen Access

Globalization of Perturbative Chern–Simons Theory on the Moduli Space of Flat Connections in the BV Formalism

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Authors

PMPavel MnëvUniversity of Notre Dame KWKonstantin WernliTwitter (United States)

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Implication

Mathematical physics analysis demonstrates globalized perturbative Chern–Simons theory across flat connection moduli, uncovering a metric-independent 3-manifold invariant.

Key Points

To globalize the perturbative path integral of Chern–Simons theory over the moduli space of flat connections within the Batalin–Vilkovisky (BV) framework.
Expanded the perturbative Chern–Simons path integral in Lorenz gauge around non-acyclic flat connections over the smooth irreducible moduli stratum.
Constructed an extension of the partition function to a nonhomogeneous form on the configuration space of kinetic flat connections, gauge-fixing flat connections, and Riemannian metrics.
Evaluated horizontality conditions with respect to the Grothendieck connection and a Gauss–Manin superconnection incorporating the BV operator.
Demonstrated that the effective BV action on zero-modes is horizontal with respect to the Grothendieck connection modulo BV-exact corrections.
Derived a global partition function volume form on the smooth irreducible moduli stratum whose cohomology class is metric-independent, yielding a topological 3-manifold invariant.

Cite This Study

Mnëv et al. (2026) studied this question.

synapsesocial.com/papers/6a93efc06c1a8fb52e79bd14 https://doi.org/10.1007/s00220-026-05727-w

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Implication

Mathematical physics analysis demonstrates globalized perturbative Chern–Simons theory across flat connection moduli, uncovering a metric-independent 3-manifold invariant.

Globalization of Perturbative Chern–Simons Theory on the Moduli Space of Flat Connections in the BV Formalism

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Implication

Key Points

Cite This Study

Globalization of Perturbative Chern–Simons Theory on the Moduli Space of Flat Connections in the BV Formalism

Discussion

Member takes

Implication

Key Points

Cite This Study

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