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Democratic actions with scalar fields: symmetric sigma models, supergravity actions and the effective theory of the type IIB superstring
by Jose Juan FernandezMelgarejo, Giacomo Giorgi, Carmen GomezFayren, Tomas Ortin, Matteo Zatti
Submission summary
Authors (as registered SciPost users):  Tomás Ortín 
Submission information  

Preprint Link:  https://arxiv.org/abs/2401.00549v2 (pdf) 
Date submitted:  20240408 12:21 
Submitted by:  Ortín, Tomás 
Submitted to:  SciPost Physics Core 
Ontological classification  

Academic field:  Physics 
Specialties: 

Approach:  Theoretical 
Abstract
The dualization of the scalar fields of a theory into (d2)form potentials preserving all the global symmetries is one of the main problems in the construction of democratic pseudoactions containing simultaneously all the original fields and their duals. We study this problem starting with the simplest cases and we show how it can be solved for scalars parametrizing Riemannian symmetric sigmamodels as in maximal and halfmaximal supergravities. Then, we use this result to write democratic pseudoactions for theories in which the scalars are nonminimally coupled to (p+1)form potentials in any dimension. These results include a proposal of democratic pseudoaction for the generic bosonic sector of 4dimensional maximal and halfmaximal ungauged supergravities. Furthermore, we propose a democratic pseudoaction for the bosonic sector of N=2B,d=10 supergravity (the effective action of the type IIB superstring theory) containing two 0, two 2, one 4, two 6 and three 8forms which is manifestly invariant under global SL(2,R) transformations.
Current status:
Reports on this Submission
Strengths
.
Report
In this manuscript the authors elaborated pseudoaction approach to the democratic formulation of supergravity theories with emphasis on supergravity theories the actions of which include both scalars, (d2)forms dual to these on the mass shell and terms describing interaction of scalars with themselves and with other pforms. In particular, the democratic pseudoaction for 10d type IIB supergravity including 0forms, 2forms, 4forms with selfdual field strength as well as 6form and 8form dual to the first two, is presented.
As authors notice in the Introduction, the 'true' actions with auxiliary fields have been known for such cases, including IIB supergravity [21,22], in the frame of PST approach [20] and other approaches some of which were reviewed in [23] (and more in recent [JHEP05(2024)320 ePrint: 2402.06947 [hepth]]). However, the pseudoaction approach of this manuscript, which does not involve auxiliary fields but imply imposing of generalized duality and selfduality conditions by hand, after obtaining equations of motion [28], may be useful in some circumstances, particularly due to its relative simplicity, and hence also deserves to be developed.
The presentation is very good and clear. I recommend this paper for publication in Science Post in its present form.
Recommendation
Publish (easily meets expectations and criteria for this Journal; among top 50%)
Strengths
1) The paper systematically addresses different dualisations in Supergravity theories.
2) The authors suggest symmetryenhancing formulations using different pseudoactions.
Weaknesses
1) The paper concentrates only on the pseudoaction approaches, while several approaches are available currently for democratic formulations with proper actions (using auxiliary fields).
2) Some comments about the earlier literature are not completely correct.
Report
The paper is well written and is a decent piece of work worth publishing in the SciPost Physics.
We have found a few minor misprints or incorrect statements.
Requested changes
1) In footnote 3, the authors refer to references [18,19] as related to nonlinear electrodynamics. The reference [19], however, covers democratic Lagrangians for arbitrary pforms (and their duals) in arbitrary dimensions. The results of [19] could be used to formulate proper actions for the systems described in the current work via pseudoactions. For the free fields, this approach was introduced in K. Mkrtchyan '19 and discussed in detail for arbitrary pforms and (dp2)form duals in S. Bansal, O. Evnin, K. Mkrtchyan '21.
2) In the third paragraph of page 3,
"... relations between (d + 1) and (d − p − 3)forms..."
should be
"... relations between (p + 1) and (d − p − 3)forms...".
3) Statements like
"The selfduality of the 5form field strength forbids the existence of a covariant action and one must necessarily work with equations of motion." (page 28)
are incorrect, given that there are covariant actions for selfdual fields, some of which are quoted in this work. We believe the authors want to stress the absence of covariant actions without auxiliary fields, but the current statement is too strong.
4) In the next to last paragraph of page 36,
"... known to exist an play an important role..."
should be
"... known to exist and play an important role..."
Recommendation
Ask for minor revision
Author: Tomás Ortín on 20240808 [id 4680]
(in reply to Report 1 on 20240716)We would like to thank the referee for the constructive comments.
We have implemented all the referee's suggestions, adding the references mentioned in his/her first comment, modifying the sentence mentioned in the third comment and fixing the misprints mentioned in the other two comments.
We have also added another reference that reviews the PST method:
C. Ferko, S. M. Kuzenko, K. Lechner, D. P. Sorokin and G. Tartaglino
Mazzucchelli, “Interacting chiral form field theories and TTlike flows in six
and higher dimensions,” JHEP 05 (2024), 320 [arXiv:2402.06947 [hepth]].
This reference complements reference [23] in the previous version (which now has become [25] after the addition of the other two references. These references are in footnote 4 in page 3.
Finally, we have corrected four equations: 5.24c, 5.24d, 5.37c and 5.37d which contained some errors that did not influence the main results of the paper.
We hope the paper can be now be published.
Attachment:
DUALSCALARS.pdf