A
bstract
All solutions of the no-birefringence conditions for nonlinear electrodynamics are found. In addition to the known Born-Infeld and Plebanski cases, we find a “reverse Born-Infeld” case, ...which has a limit to Plebanski, and an “extreme-Born-Infeld” case, which arises as a Lagrangian constraint. Only Born-Infeld has a weak-field limit, and only Born-Infeld and extreme-Born-Infeld avoid superluminal propagation in constant electromagnetic backgrounds, but all cases have a conformal strong-field limit that coincides with the strong-field limit of Born-Infeld found by Bialynicki-Birula.
A
bstract
We compute correlation functions of chiral primary operators in
N
=
2
super-conformal theories at large
N
using a construction based on supersymmetric localization recently developed by ...Gerchkovitz et al. We focus on
N
=
4
SYM as well as on supercon-formal QCD. In the case of
N
=
4
we recover the free field theory results as expected due to non-renormalization theorems. In the case of superconformal QCD we study the planar expansion in the large
N
limit. The final correlators admit a simple generalization to a finite
N
formula which exactly matches the various small
N
results in the literature.
A
bstract
We study a new hermitian one-matrix model containing a logarithmic Penner’s type term and another term, which can be obtained as a limit from logarithmic terms. For small coupling, the ...potential has an absolute minimum at the origin, but beyond a certain value of the coupling the potential develops a double well. For a higher critical value of the coupling, the system undergoes a large
N
third-order phase transition.
A
bstract
Using supersymmetric localization, we study the sector of chiral primary operators (Tr
ϕ
2
)
n
with large
R
-charge 4
n
in
N
= 2 four-dimensional superconformal theories in the weak ...coupling regime
g
→ 0, where λ ≡
g
2
n
is kept fixed as
n
→ ∞,
g
representing the gauge theory coupling(s). In this limit, correlation functions
G
2
n
of these operators behave in a simple way, with an asymptotic behavior of the form
G
2
n
≈
F
∞
λ
λ
2
π
e
2
n
n
α
, modulo
O
(1
/n
) corrections, with
α
=
1
2
dim
g
for a gauge algebra
g
and a universal function
F
∞
(λ). As a by-product we find several new formulas both for the partition function as well as for perturbative correlators in
N
=
2
s
u
N
gauge theory with 2
N
fundamental hypermultiplets.
A
bstract
For the general theory of nonlinear electrodynamics (NLED) we prove that causality implies both the Dominant Energy Condition (DEC) and, surprisingly, the Strong Energy Condition (SEC). ...This has implications for gravitational applications, such as regular black holes supported by NLED matter. For self-dual NLED theories, weak-field causality alone implies both the DEC and SEC, as we illustrate with Born-Infeld and ModMax electrodynamics.
A
bstract
Exact results in supersymmetric Chern-Simons and
Yang-Mills theories can be used to examine the quantum behavior of observables and the structure of the perturbative series. For the U(2)
×
... U(2) ABJM model, we determine the asymptotic behavior of the perturbative series for the partition function and write it as a Borel transform. Similar results are obtained for
SU(2) super Yang-Mills theory with four fundamental flavors and in
super Yang-Mills theory, for the partition function as well as for the expectation values for Wilson loop and ’t Hooft loop operators (in the 0 and 1 instanton sectors). In all examples, one has an alternate perturbation series where the coefficient of the
n
th term increases as
n
!, and the perturbation series are Borel summable. We also calculate the expectation value for a Wilson loop operator in the
SU(
N
) theory at large
N
in different regimes of the ’t Hooft gauge coupling and mass parameter. For large masses, the calculation reproduces the running gauge coupling for the pure
SYM theory.
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