A note on membrane interactions and the scalar potential
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Springer
Received: July 6, 2020 Accepted: September 1, 2020 Published: October 1, 2020
Alvaro Herraez Departamento de F´ısica Te´ orica and Instituto de F´ısica Te´ orica UAM/CSIC, Universidad Aut´ onoma de Madrid, Cantoblanco, 28049 Madrid, Spain
E-mail: [email protected] Abstract: We compute the tree-level potential between two parallel p-branes due to the exchange of scalars, gravitons and (p+1)-forms. In the case of BPS membranes in 4d N = 1 supergravity, this provides an interesting reinterpretation of the classical Cremmer et al. formula for the F-term scalar potential in terms of scalar, graviton and 3-form exchange. In this way, we present a correspondence between the scalar potential at every point in scalar field space and a system of two interacting BPS membranes. This could potentially lead to interesting implications for the Swampland Program by providing a concrete way to relate conjectures about the form of scalar potentials with conjectures regarding the spectrum of charged objects. Keywords: Flux compactifications, p-branes, Supersymmetric Effective Theories ArXiv ePrint: 2006.01160
c The Authors. Open Access, Article funded by SCOAP3 .
https://doi.org/10.1007/JHEP10(2020)009
JHEP10(2020)009
A note on membrane interactions and the scalar potential
Contents 1
2 Interactions between Dp-branes in D dimensions 2.1 The scalar plus graviton interaction 2.2 The q-form interaction 2.3 Relation with the WGC for q-forms in the presence of dilaton-like couplings
2 3 5 7
3 The 4d N = 1 scalar potential in terms of membranes 3.1 The scalar potential and the 3-form interaction 3.2 The scalar and graviton interaction
8 8 9
4 Summary and outlook
1
11
Introduction
It is well known that the 4d cosmological constant can be interpreted in terms of field strengths of 3-forms. Even though they do not propagate additional degrees of freedom, they can acquire non-vanishing vevs and give rise to a cosmological constant contribution. For this reason, 3-forms have been used in trying to solve the cosmological constant problem as in [1–5]. More specifically, considering the membranes to which a 3-form naturally couples provides a mechanism for the cosmological constant to change when a membrane is crossed, as considered originally in [6, 7], and also in [8] within the context of String Theory. In fact, this relation works and has been studied not only for constant contributions but for more general scalar potentials including axions in [9–14]. In String Theory, this has also been explored [15–21] and in the context of type II compactifications with fluxes, it was shown in [22, 23] that the complete F-term flux potential can be expressed, after integrating out the 4-forms, as 1 V = Z AB QA QB , (1.1) 2 where Z AB includes the field dependence and can be obtained from the kinetic terms of the 3-forms. The QA give the couplings of the corresponding 4-form. The fact that this N = 1 potential can be expressed completely in terms of 3-forms, which naturally couple to membranes, suggests that a direct relation
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