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Generalized lattices, conformal manifolds, and symmetries
by Shlomo S. Razamat, Michal Shemesh, and Aelly Zeltzer
This is not the latest submitted version.
Submission summary
| Authors (as registered SciPost users): | Shlomo Razamat |
| Submission information | |
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| Preprint Link: | scipost_202504_00018v1 (pdf) |
| Date submitted: | April 10, 2025, 9:03 p.m. |
| Submitted by: | Razamat, Shlomo |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
We consider supersymmetric conformal quantum field theories (SCFTs) with degrees of freedom labeled by lattice data. We will assume that in terms of the corresponding lattice the interactions are nearest neighbor and exactly marginal. For example, one can construct such theories by coupling many copies of a single SCFT with exactly marginal deformations. In particular, we discuss the interplay between conformal manifolds of such theories and their global, on-site and lattice, symmetries. We show that one can interpret certain current non-conservation equations for symmetries broken by the interactions as conservation equations including the lattice directions. Moreover, we discuss a class of exactly marginal deformations which are labeled by lattice holonomies that are topological on the lattice. We discuss concrete examples of such constructions and comment on their relevance to compactifications of SCFTs.
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
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Requested changes
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The discussion of the duality depicted in Figure 5 (Section 7.2) bears a strong resemblance to the "duality" (or more precisely, the continuation past infinite coupling) in the context of five-brane webs. It is known that the theory associated with a punctured sphere can be realized using such five-brane webs (see, for example, arXiv:0906.0359). The authors should comment on this potential connection. Furthermore, it would be valuable for the authors to clarify whether the superpotentials of the theory before and after applying the duality are related by Seiberg duality.
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A number of minor typographical errors should be corrected throughout the manuscript:
Page 2: "in in" should be "in". Page 4: "bares more resemblances" should be "bears more resemblance". Page 5: "it’s own O(2) symmetry" should be "its own O(2) symmetry". Page 8: "npdes" should be "nodes". Page 11: "the symmstry is extended" should be "the symmetry is extended". Page 11: "the the marginal superpotential" should be "the marginal superpotential". Page 13: "higer dimensional lattices" should be "higher-dimensional lattices". Page 13: "these marginal opertators" should be "these marginal operators". Page 13: "one obtaines" should be "one obtains". Page 13: "large enough value the flux" should be "large enough value of the flux". Page 16: "operators corersponding to paths" should be "operators corresponding to paths". Page 23: "several question" should be "several questions". Page 24: "it’s Cartan sub-group" should be "its Cartan subgroup".
Recommendation
Ask for minor revision
Strengths
- makes the very interesting observation that SCFT's defined by a lattice constructed by joining elementary SCFT's can naturally exhibit higher-dimensional behavior in the form of current non-conservation equations being interpreted as conservation equations in higher dimensions
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In the results presented in the paper, it seems very relevant that the lattice (the quiver) is periodic. For instance, the topological charge operator in the lattice direction relies on the lattice being periodic (in that respect, would the (non)-conservation equations around eq. (11) be different for the boundaries of an open lattice?). Can open lattices can still host similar symmetries, perhaps upon adding suitable boundary conditions”?
The case in section 5.2 seems to include the Z_N orbifold of the conifold (more generically, section 6 seems to include Z_NxZ_M orbifolds of the conifold), which is a deformation of the N=2 necklace quiver briefly mentioned in footnote 20. Even though perhaps beyond the scope of the paper, it is natural to wonder about the string theory interpretation of the higher-dimensional symmetry found in the paper. In addition, given the relation to the N=2 necklace quiver, it is natural to wonder about its meaning in the context of standard deconstruction. Another natural question, also probably beyond the scope of the paper, is whether these symmetries can be gauged.
The paper presents interesting novel ideas and it is well-written. I find the paper very interesting and recommend it for publication.
Requested changes
Typos:
- page 8, 7th line from top: "npdes" -> nodes
- page 21, 16th line from bottom: "continues" -> continuous
Recommendation
Publish (easily meets expectations and criteria for this Journal; among top 50%)
We are grateful to the referee for their time and the thoughtful comments on the manuscript.
1) Even in presence of the boundary a symmetry is preserved and conservation equation 11 is true in the bulk of the lattice. On the boundary indeed it needs to be corrected. Whether a chain is open or closed has an important effect on counting exactly marginal operators: this is an avatar of the referees comment. This change in counting of exactly marginal operators is directly related to the conservation equation being different on the boundary. We discuss this aspect of the open chain in the fourth paragraph on page 8 and in footnote 14.
2) Indeed, at least some of the constructions we discuss have brane realizations and it would be very interesting to understand our claims in that context. In this paper, as it is purely field theoretical, we left such considerations for future work. Let us stress here that deconstruction is importantly different from what we are doing: here we insist on not breaking the conformal symmetry while performing our manipulations, while deconstruction (though starting with similar conformal lattices of QFTs) involves turning on vacuum expectation values (and thus breaking conformality) when taking the continuum limit.
3) We thank the referee for stressing the importance of understanding gauging of symmetries. Understanding various anomalies of lattice symmetries and "on site'' symmetries in such constructions is one of our main goals for extending this research.
We would like to thank the referee for the interesting comments.
Author: Shlomo Razamat on 2025-07-22 [id 5659]
(in reply to Report 2 on 2025-06-09)We are grateful to the referee for the careful reading of the manuscript and their comments.
1) As all the manipulations discussed in the paper preserve conformality, the dualities we discuss are not IR/Seiberg ones, but rather conformal. We will add a footnote stressing this point.
2) We thank the referee for suggesting to mention brane webs: indeed although our discussion is more general, in some cases the duality manipulations we mention can have brane avatars. We will add a footnote mentioning this fact.
We thank again the referee for the physics comments and catching the typos.