A Systematic Approach to Consistent Truncations of Supergravity Theories

Round 1

Reviewer 1 Report

This is an excellent paper, that nicely discusses, summarises and reviews the new and powerful methodology of constructing consistent truncations coming from exceptional generalised geometry. While some parts of this paper are published elsewhere, it is excellent to have all these exciting and timely results and methods brought together in a concise and clear formulation.

I only have some minor suggestions for improvements, which are mostly typos I have found and points that can be elaborated on by the author. I want to highlight these to facilitate the proofing process. However, I believe the article can also be published as-is if the author chooses to do so.

Line 11: "in string", the word "theory" is missing.

Line 23: "truncated" -> "truncate".

Line 25: "a" missing before clear.

Line 26: "by" missing after "obtained".

Line 53: There seems to be some LaTex problem here as the sentence is incomprehensible and the reference is missing.

Line 67: "by" missing after "obtained".

Line 85: missing reference.

Line 91: one of the "{\cal N}=4" should be "{\cal N}=2".

Line 109-110: the singlet intrinsic torsion should also be constant!

Equations (3), (7), (11): O(d) vs SO(d)

Line 165: It would be good to define adj F clearly, maybe above (13)? 

Line 172: For ordinary G-structures, it is always possible to reduce a structure group to its maximal compact subgroup (although typically no canonical choice for the invariant tensor exists). This is equivalent to the fact that any Riemannian manifold admits a Riemannian metric. In terms of G-structures, the statement relies on the fact that any non-compact group is contractible to its compact subgroup. Presumably the same is true for generalised G-structures, which are just G-structures on generalised tangent bundles. So is it right that considering G_s \subset H_d is not a restriction and can always be done? If so, perhaps this could be emphasised.

Lines 208 - 210: should mention that the singlet intrinsic torsion must be constant.

Line 250: missing "the" before "algebra".

Equation (32) on RHS: M N indices should be up, not down.

Lines 268 - 278: A version of this proof first appeared in reference [18] for 1/2-max truncations. Perhaps, therefore, [18] could be cited alongside [20] here.

Lines 305 and various throughout from there: USp vs Usp. Both are used. It would be nice to consistently use one of them.

Equations (61), (66), (67), (68), (69), (81): missing comma between equations.

Above (96): missing "a" or "the" between "we can also derive" and "metric"

Line 385: maybe "Wolf spaces" rather than "Wolf space"?

Line 391: perhaps refer to table 2 explicitly?

Line 440: Is the author referring to differential conditions like those that were derived in [19]? Or does the author have in mind something like [11]? If so, perhaps these could be cited.

Last sentence before references: Missing reference again.

Author Response

Let me first thank for the thorough reading of the manuscript and the comments. I made almost all the modifications requested in the report. 

There is only a comment made by the referee that I did not take into account. The referee asks whether  considering structure groups Gs that subgroups of Hd is can always be done, and, if so, why saying that we restrict to this case. The reason of my comment is that, we can always a structure group to its maximal compact subgroup, but we can also take non-compact versions of Hd by changing the definition of the generalised metric. And these cases are not of interest for this manuscript.

sincerely yours

Michela Petrini

Reviewer 2 Report

This is a thorough and well-written review of the applications of Exceptional Generalised Geometry to the construction of consistent truncations of supergravity theories to lower dimensions. I recommend its publication.

Author Response

There is nothing to reply to, it seems to me.  Thank you for the positive review.

Michela Petrini

Reviewer 3 Report

In her article, Michela Petrini reviews the use of G-structures in Exceptional Generalized Geometry 
for the systematic construction of consistent truncations. The article starts with a short review of 
G-structures in Riemannian geometry and its application to Scherk-Schwarz reductions. It proceeds to introduce 
Generalized G-structures, for which the conventional structure group must be extended to $E_{d(d)}$. 
The main part of the paper is dedicated to a systematic survey of M-theory truncations to five dimensions. 

The paper represents the state-of-the-art of the field. I definitely recommend its publication.

 

Author Response

There is nothing to reply to, it seems to me.  Thank you for the positive review.

Michela Petrini