Strings and membranes from A-theory five brane

1) The paper explains how the A-theory fivebrane action with manifest SL(6) symmetry, which the authors originally wrote down in reference [1], reduces to (the actions for) other known lower-dimensional branes expressed in duality invariant formulations, namely strings and two-branes. This is an important consistency check on this proposed A-theory formulation.

2) Calculations and results are given rather explicitly.

1) Science-wise: I am puzzled at the derivation of the "non-perturbative" M2 brane action from the A-theory fivebrane action via the "perturbative" M5 action (6.20). (Here "perturbative" means to quadratic order in derivatives and the "non-perturbative" M2 brane action is the usual Nambu-Goto style one, which features arbitrary orders in derivatives via a determinant in the lagrangian.) This apparent tension should be addressed or at least commented on.

2) Text-wise: the writing as well as the language is below par overall. The other report lists a few examples of typos and grammar/syntax issues so I will not repeat those here. There are also instances where text is duplicative or near duplicative of other text. (One that jumped at me was in the last paragraph of sec 1.1 and the first one of sec 1.2.) The arguments of this work were mostly clear, at least to this reader. However the text itself served to distract from rather than clarify and enhance the logical development of the material and I would recommend to the authors that future manuscripts should get more editorial attention both to the language of individual paragraphs as well as to how the text coheres as a whole. I found myself thinking "this was written by committee" a lot.

3) A comparatively minor quibble is that there could have been more of an effort to connect to the notation and terminology used by the Exceptional Field Theory subtopic to which this manuscript ostensibly contributes (as noted also by the other referee). In particular the use of \vartriangleright (I think) for currents is a bit distracting because one would naturally associate that symbol with e.g. a group action.

Ask for minor revision

1) The authors continue the investigation of their previous work (reference [1] in the paper), which offers a novel perspective on world-volume theories and duality symmetry in string and M-theory. Their goal here is to construct a world-volume theory that is (manifestly) duality invariant under U-duality, analogous to how Exceptional Field Theory manifests the U-duality of maximal supergravity or how F-theory makes the SL(2) symmetry of IIB supergravity manifest. They propose a new 5-brane theory in an auxiliary 10-dimensional target space, which they call the A5-brane.

2) A particularly interesting and, to my knowledge, novel observation is that the SL(5) U-duality symmetry can be enhanced to SL(6), such that the field content not only incorporates the target space geometry but also includes a world-volume geometry of a 5-brane.

3) The authors clearly demonstrate that their new A5-brane theory reproduces known world-volume theories (without manifest duality symmetry) — such as those of the string, M2-brane, and M5-brane — upon dimensional reduction of both the world-volume and target space.

4) The draft is, in general, well-written and understandable, with sufficient technical detail and a solid introduction/overview of the topic and scope of the paper.

5) The references provide a well-rounded representation of the relevant literature.

1) Since the authors focus on the low-dimensional case (D=3 in their notation), their construction results in an M5-brane theory in 4-dimensional space, which seems unusual. This raises the concern that their findings might be an artifact of the low-dimensional setting, which is not clearly addressed in the paper.

2) The paper does not engage in sufficient detail with alternative or related approaches to the problem of U-duality covariance in world-volume theories.

3) The quality of the English and general editorial state of the manuscript is subpar. In an era where automated tools can assist with grammar and style checking, the presence of numerous typos and syntactic issues that hinder readability is unnecessary and should be corrected.

A few examples:

Page 6, last paragraph of section 1.2: "In section 6 we begin by the SL(6) covariant A5-brane Lagrangian to lead the new perturbative M5-brane Lagrangian." -> Suggested revision: "In section 6, we begin with the SL(6)-covariant A5-brane Lagrangian, which leads to a new perturbative M5-brane Lagrangian."

Page 38, point 4: "Quantizaion" --> "Quantization"

Page 38, point 5, last sentence: "Constructing A-theory may give a hint of new description of string." -> Suggested revision: "Constructing A-theory may provide a hint toward a new description of string theory."

4) As in the authors’ previous work (or collaborations among them), the paper uses a notation that diverges from the conventions used by much of the double field theory / exceptional field theory community. While their notation appears consistent and in some cases predates others in the literature, this deviation may hinder accessibility and readability.

1) Clarify dimensional dependence and generalisation potential: The authors should more clearly explain the implications of working in low dimensions (D=3), particularly how they obtain an M5-brane theory in 4-dimensional space, which seems nonstandard. They should also discuss whether the enhancement from SL(5) to SL(6) is a feature unique to low-dimensional settings, or if similar enhancements are expected for higher dimensions. Relevant literature discussing enhanced dualities in low-dimensional brane settings should be cited and discussed, e.g.:

    M. Duff and J. Lu, Duality rotations in membrane theory, Nucl. Phys. B347 (1990) 394–419

    M.J. Duff, J.X. Lu, R. Percacci, C.N. Pope, H. Samtleben, and E. Sezgin, Membrane Duality Revisited, [arXiv:1509.02915]

2) Discuss relation to existing approaches: Although the literature is broadly cited, a more explicit discussion of how the authors’ approach compares with other attempts to formulate U-duality covariant world-volume theories is needed. For example, a discussion of the differences and connections with works such as [47] and [62] (as numbered in their paper) would significantly strengthen the context and relevance of the present work.

3) Thorough proofreading and language polishing: The manuscript should be carefully proofread to correct grammatical and typographical errors, which currently detract from the clarity and flow of the presentation.

Ask for minor revision