More on the weak gravity conjecture via convexity of charged operators
(2021) In Journal of High Energy Physics 2021(12).- Abstract
The Weak Gravity Conjecture has recently been re-formulated in terms of a particle with non-negative self-binding energy. Because of the dual conformal field theory (CFT) formulation in the anti-de Sitter space, the conformal dimension ∆(Q) of the lowest-dimension operator with charge Q under some global U(1) symmetry must be a convex function of Q. This property has been conjectured to hold for any (unitary) conformal field theory and generalized to larger global symmetry groups. Here we refine and further test the convex charge conjecture via semiclassical computations for fixed charge sectors of different theories in various dimensions. We analyze the convexity properties of the leading and next-to-leading order terms stemming from... (More)
The Weak Gravity Conjecture has recently been re-formulated in terms of a particle with non-negative self-binding energy. Because of the dual conformal field theory (CFT) formulation in the anti-de Sitter space, the conformal dimension ∆(Q) of the lowest-dimension operator with charge Q under some global U(1) symmetry must be a convex function of Q. This property has been conjectured to hold for any (unitary) conformal field theory and generalized to larger global symmetry groups. Here we refine and further test the convex charge conjecture via semiclassical computations for fixed charge sectors of different theories in various dimensions. We analyze the convexity properties of the leading and next-to-leading order terms stemming from the semiclassical computation, de facto, extending previous tests beyond the leading perturbative contributions and to arbitrary charges. In particular, the leading contribution is sufficient to test convexity in the semiclassical computations. We also consider intriguing cases in which the models feature a transition from real to complex conformal dimensions either as a function of the charge or number of matter fields. As a relevant example of the first kind, we investigate the O(N) model in 4 + ϵ dimensions. As an example of the second type, we consider the U(N) × U(M) model in 4 − ϵ dimensions. Both models display a rich dynamics where, by changing the number of matter fields and/or charge, one can achieve dramatically different physical regimes. We discover that whenever a complex conformal dimension appears, the real part satisfies the convexity property.
(Less)
- author
- Antipin, Oleg ; Bersini, Jahmall ; Sannino, Francesco ; Wang, Zhi Wei LU and Zhang, Chen
- organization
- publishing date
- 2021-12
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- Conformal and W Symmetry, Conformal Field Theory, Global Symmetries
- in
- Journal of High Energy Physics
- volume
- 2021
- issue
- 12
- article number
- 204
- publisher
- Springer
- external identifiers
-
- scopus:85122077311
- ISSN
- 1029-8479
- DOI
- 10.1007/JHEP12(2021)204
- language
- English
- LU publication?
- yes
- additional info
- Publisher Copyright: © 2021, The Author(s).
- id
- 67872818-f88c-4ee6-9f5f-775e1b16718c
- date added to LUP
- 2022-01-28 09:37:50
- date last changed
- 2024-04-20 19:42:32
@article{67872818-f88c-4ee6-9f5f-775e1b16718c,
abstract = {{<p>The Weak Gravity Conjecture has recently been re-formulated in terms of a particle with non-negative self-binding energy. Because of the dual conformal field theory (CFT) formulation in the anti-de Sitter space, the conformal dimension ∆(Q) of the lowest-dimension operator with charge Q under some global U(1) symmetry must be a convex function of Q. This property has been conjectured to hold for any (unitary) conformal field theory and generalized to larger global symmetry groups. Here we refine and further test the convex charge conjecture via semiclassical computations for fixed charge sectors of different theories in various dimensions. We analyze the convexity properties of the leading and next-to-leading order terms stemming from the semiclassical computation, de facto, extending previous tests beyond the leading perturbative contributions and to arbitrary charges. In particular, the leading contribution is sufficient to test convexity in the semiclassical computations. We also consider intriguing cases in which the models feature a transition from real to complex conformal dimensions either as a function of the charge or number of matter fields. As a relevant example of the first kind, we investigate the O(N) model in 4 + ϵ dimensions. As an example of the second type, we consider the U(N) × U(M) model in 4 − ϵ dimensions. Both models display a rich dynamics where, by changing the number of matter fields and/or charge, one can achieve dramatically different physical regimes. We discover that whenever a complex conformal dimension appears, the real part satisfies the convexity property.</p>}},
author = {{Antipin, Oleg and Bersini, Jahmall and Sannino, Francesco and Wang, Zhi Wei and Zhang, Chen}},
issn = {{1029-8479}},
keywords = {{Conformal and W Symmetry; Conformal Field Theory; Global Symmetries}},
language = {{eng}},
number = {{12}},
publisher = {{Springer}},
series = {{Journal of High Energy Physics}},
title = {{More on the weak gravity conjecture via convexity of charged operators}},
url = {{http://dx.doi.org/10.1007/JHEP12(2021)204}},
doi = {{10.1007/JHEP12(2021)204}},
volume = {{2021}},
year = {{2021}},
}