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Twisted holography on AdS$_3 \times S^3 \times K3$ & the planar chiral algebra
by Víctor E. Fernández, Natalie M. Paquette, Brian R. Williams
Submission summary
Authors (as registered SciPost users):  Natalie Paquette 
Submission information  

Preprint Link:  https://arxiv.org/abs/2404.14318v1 (pdf) 
Date submitted:  20240627 23:39 
Submitted by:  Paquette, Natalie 
Submitted to:  SciPost Physics 
Ontological classification  

Academic field:  Physics 
Specialties: 

Approach:  Theoretical 
Abstract
In this work, we revisit and elaborate on twisted holography for AdS$_3 \times S^3 \times X$ with $X= T^4$, K3, with a particular focus on K3. We describe the twist of supergravity, identify the corresponding (generalization of) BCOV theory, and enumerate twisted supergravity states. We use this knowledge, and the technique of Koszul duality, to obtain the $N \rightarrow \infty$, or planar, limit of the chiral algebra of the dual CFT. The resulting symmetries are strong enough to fix planar 2 and 3point functions in the twisted theory or, equivalently, in a 1/4BPS subsector of the original duality. This technique can in principle be used to compute corrections to the chiral algebra perturbatively in $1/N$.
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 multipronged followup work
 Detail a groundbreaking theoretical/experimental/computational discovery
 Present a breakthrough on a previouslyidentified and longstanding research stumbling block
Current status:
Reports on this Submission
Strengths
1) The paper is very beautifully written. The authors do a pretty good job of explaining foundational details concerning their work, so, although it is a long and rather technical paper, it is comparatively readable for a paper on this subject.
2) I think what the authors are doing is a valuable contribution to our understanding of the string theory background that they are studying and its intereesting dualities.
Weaknesses
The paper is certainly not an easy read. But given the nature of the topic, I am not sure that the authors could be expected to do better at making it readable, so I am not sure I would really call that a weakness.
Report
I think the paper does meet the acceptance criteria of the journal and I do recommend publication. I have a couple of comments and a question.
Nontrivial comment: In general, I think that there is something that isn't well expressed in the literature on twisted holography. This is what it really means to ``give a VEV to the superghost.'' In quantum field theory in general, what it means to ``give a VEV'' to a field is the following: first, this only makes sense if one is working on a noncompact space with one or more asymptotic regions ``at infinity.'' Assuming this, what it means to ``give a VEV'' to a field is to specify the asymptotic value of the field at infinity; the theory then decides for itself what will happen in the interior. (If there is more than one asymptotic region at infinity, in general one can specify different asymptotic values at different ends.)
What I have written is no problem for this paper, because the authors are working on the noncompact manifold C^3 x K3, but note that if one is on a compact CalabiYau fivefold, I do not believe that ``twisted holography'' can be defined as there is no asymptotic region and no way to ``give a VEV'' to anything. I believe the paper could be improved by more accurately saying at the beginning what it means to ``give a VEV.'' But this isn't a comment just on this paper; it is a comment on the whole literarature on twisted holography.
Trivial comment: On p. 21, is eqn. (2.5.11) written correctly? I think the authors intend to have a first order differential operator acting on Phi, but for this they need parentheses. I also was confused about C^{22} at the top of the page. Please note that this isn't intended as a comprehensive list of possible minor misprints.
And a question: What would happen if T^4 or K3 is replaced by a Hopf surface
S^3 x S^1? Note that string theory on AdS_3 x S^3 x S^3 x S^1 is comparatively not well understood at all. Is there something useful to say?
Recommendation
Publish (surpasses expectations and criteria for this Journal; among top 10%)