SciPost Submission Page
BCOV on the Large Hilbert Space
by Eugenia Boffo, Ondřej Hulík, Ivo Sachs
Submission summary
| Authors (as registered SciPost users): | Eugenia Boffo |
| Submission information | |
|---|---|
| Preprint Link: | scipost_202506_00042v2 (pdf) |
| Date submitted: | Feb. 5, 2026, 10:08 a.m. |
| Submitted by: | Eugenia Boffo |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
We formulate the BCOV theory of deformations of complex structures as a pull-back to the super moduli space of the worldline of a spinning particle. In this approach the appearance of a non-local kinetic term in the target space action has the same origin as the mismatch of pictures in the Ramond sector of super string field theory and is resolved by the same type of auxiliary fields in shifted pictures. The BV-extension is manifest in this description. A compensator for the holomorphic 3-form can be included by resorting to a description in the large Hilbert space.
Author indications on fulfilling journal expectations
- Provide a novel and synergetic link between different research areas.
- Open a new pathway in an existing or a new research direction, with clear potential for multi-pronged follow-up work
- Detail a groundbreaking theoretical/experimental/computational discovery
- Present a breakthrough on a previously-identified and long-standing research stumbling block
Author comments upon resubmission
We have made several improvements in the exposition and clarified the points raised by Referee2. The main results are not changed but are streamlined now.
List of changes
In the introduction, we have removed many other side remarks that are not relevant for the result, and clarified that the original formulation of BCOV is indeed complicated rather by the fact that it cannot be formulated as a (Maurer-Cartan type) string field theory action. In fact, the latter requires a pairing compatible with a cyclic cohomology, rather than a degree preserving one.
We have clarified in the introduction (1st paragraph in page 2) as well as in section 3.3, that the theory, formulated in the small Hilbert space, leads to a Poisson degenerate BV-theory, expressed in terms of potentials (and harmonic polyvectors). We also added an extra paragraph (the 4th from the end) in the introduction to highlight this.
We have commented on pre-existing results and literature in the introduction and throughout the main text, following the valuable explanation of Referee2.
About the list of major points that Referee2 wanted to be addressed:
-- Formulation of the field theories has been streamlined and unambiguously defined;
-- We clarified that the theory formulated in section 3 is a degenerate Poisson BV theory. For the theory in section 4, this has also been noticeably changed: we have listed the fields involved, assigned them their parity, explained what kind of bracket we have used. The main result remains the same: we can present a field theory of complex structure deformations preserving the holomorphic volume form, that satisfies a master equation with that bracket.
-- Concerning the question of the relationship between our model and dimensional reduction of the sigma model, we added a remark in section 3.2. to point out that our starting point is indeed different. The sigma model is defined directly on the moduli space and therefore lacks the β- and γ superghosts which play an important role in our construction.
-- We reinstated the gradings, but it is unavoidable to work with two different conventions between sec. 3 and 4. Regarding the "even differentials", we clarified that the derivative operator under inspection has a nilpotent left action and even parity.
-- Notation abuse issue: we have accepted the suggestion and got rid of $\partial_\Upsilon$.
-- We think we improved the presentation significantly. Introduction, body and conclusion have been substantially changed.
-- For the review on pictures, this is now in a paragraph in sec 3.2.
About the most pressing minor remark of Referee2:
-- We added some explanation and references on the claim that Dolbeault cohomology of polyvectors on a CY is the same as when the polyvectors are restricted to ker div.
We have clarified in the introduction (1st paragraph in page 2) as well as in section 3.3, that the theory, formulated in the small Hilbert space, leads to a Poisson degenerate BV-theory, expressed in terms of potentials (and harmonic polyvectors). We also added an extra paragraph (the 4th from the end) in the introduction to highlight this.
We have commented on pre-existing results and literature in the introduction and throughout the main text, following the valuable explanation of Referee2.
About the list of major points that Referee2 wanted to be addressed:
-- Formulation of the field theories has been streamlined and unambiguously defined;
-- We clarified that the theory formulated in section 3 is a degenerate Poisson BV theory. For the theory in section 4, this has also been noticeably changed: we have listed the fields involved, assigned them their parity, explained what kind of bracket we have used. The main result remains the same: we can present a field theory of complex structure deformations preserving the holomorphic volume form, that satisfies a master equation with that bracket.
-- Concerning the question of the relationship between our model and dimensional reduction of the sigma model, we added a remark in section 3.2. to point out that our starting point is indeed different. The sigma model is defined directly on the moduli space and therefore lacks the β- and γ superghosts which play an important role in our construction.
-- We reinstated the gradings, but it is unavoidable to work with two different conventions between sec. 3 and 4. Regarding the "even differentials", we clarified that the derivative operator under inspection has a nilpotent left action and even parity.
-- Notation abuse issue: we have accepted the suggestion and got rid of $\partial_\Upsilon$.
-- We think we improved the presentation significantly. Introduction, body and conclusion have been substantially changed.
-- For the review on pictures, this is now in a paragraph in sec 3.2.
About the most pressing minor remark of Referee2:
-- We added some explanation and references on the claim that Dolbeault cohomology of polyvectors on a CY is the same as when the polyvectors are restricted to ker div.
Current status:
In refereeing