A
bstract
We consider Schur line defect correlators in four dimensional
N
= 4 U(
N
) SYM and their giant graviton expansion encoding finite
N
corrections to the large
N
limit. We compute in closed ...form the single giant graviton contribution to correlators with general insertions of
1
2
-BPS charged Wilson lines. For the 2-point function with fundamental and anti-fundamental Wilson lines, we match the result from fluctuations of two half-infinite strings ending on the giant graviton, recently proposed in arXiv:2403.11543. In particular, we prove exact factorization of the defect contribution with respect to wrapped D3 brane fluctuations representing the single giant graviton correction to the undecorated Schur index. This follows from a finite-difference representation of the Schur line defect index in terms of the index without defects, and similar factorization holds quite generally for more complicated defect configurations. In particular, the single giant graviton contribution to the 4-point function with two fundamental and two anti-fundamental lines is computed and discussed in this perspective.
A
bstract
Starting with some known localization (matrix model) representations for correlators involving 1/2 BPS circular Wilson loop
W
in
N
= 4 SYM theory we work out their 1
/N
expansions in the ...limit of large ’t Hooft coupling
λ
. Motivated by a possibility of eventual matching to higher genus corrections in dual string theory we follow arXiv:2007.08512 and express the result in terms of the string coupling
g
s
∼
g
YM
2
∼
λ
/
N
and string tension
T
∼
λ
. Keeping only the leading in 1/
T
term at each order in
g
s
we observe that while the expansion of
W
is a series in
g
s
2
/
T
, the correlator of the Wilson loop with chiral primary operators
O
J
has expansion in powers of
g
s
2
/
T
2
. Like in the case of
W
where these leading terms are known to resum into an exponential of a “one-handle” contribution
∼
g
s
2
/
T
, the leading strong coupling terms in
WO
J
sum up to a simple square root function of
g
s
2
/
T
2
. Analogous expansions in powers of
g
s
2
/
T
are found for correlators of several coincident Wilson loops and they again have a simple resummed form. We also find similar expansions for correlators of coincident 1/2 BPS Wilson loops in the ABJM theory.
A
bstract
We consider the Schur index of
N
= 4 U(
N
) SYM theory in 4d and its holographic giant graviton-type expansion at finite
N
. We compute the world-volume brane superconformal index by a ...recently proposed definition of the gauge holonomy integral as a multivariate residue. This is evaluated by a novel deformation algorithm that avoids Gröbner basis methods. Various terms of the brane expansion are computed and their sum is shown to be free of wall-crossing singularities to the order we explored. The relation between the brane expansion and previous giant graviton-type represenations of the Schur index is clarified.
A
bstract
The flavored superconformal Schur index of
N
= 4 U(
N
) SYM has finite
N
corrections encoded in its giant graviton expansion in terms of D3 branes wrapped in
AdS
5
×
S
5
. The key element ...of this decomposition is the non-trivial index of the theory living on the wrapped brane system. A remarkable feature of the Schur limit is that the brane index is an analytic continuation of the flavored index of
N
= 4 U(
n
) SYM, where
n
is the total brane wrapping number. We exploit recent exact results about the Schur index of
N
= 4 U(
N
) SYM to evaluate the closed form of the brane indices appearing in the giant graviton expansion. Away from the unflavored limit, they are characterized by quasimodular forms providing exact information at all orders in the index universal fugacity. As an application of these results, we present novel exact expressions for the giant graviton expansion of the unflavored Schur index in a class of four dimensional
N
= 2 theories with equal central charges
a
=
c
, i.e. the non-Lagrangian theories
Γ
̂
SU
N
with Γ =
E
6
,
E
7
,
E
8
.
A
bstract
We consider four dimensional U(
N
)
N
= 4 SYM theory interacting with a 3d
N
= 4 theory living on a codimension-one interface and holographically dual to the D3-D5 system without flux. ...Localization captures several observables in this dCFT, including its free energy, related to the defect expectation value, and single trace
1
2
-BPS composite scalars. These quantities may be computed in a hermitian one-matrix model with non-polynomial single-trace potential. We exploit the integrable Volterra hierarchy underlying the matrix model and systematically study its 1/
N
expansion at any value of the ’t Hooft coupling. In particular, the strong coupling regime is determined — up to non-perturbative exponentially suppressed corrections — by differential relations that constrain higher order terms in the 1/
N
expansion. The analysis is extended to the model with SU(
N
) gauge symmetry by resorting to the more general Toda lattice equations.
A
bstract
We consider the refined Schur superconformal index of 4d
N
= 4 U(
N
) SYM and the first term of its giant-graviton expansion, first predicted in arXiv:2001.11667 using indirect ...superconformal algebra considerations and analytic continuation of fugacities. This correction is the leading non-perturbative correction to the index at large
N
and we reproduce it from the semiclassical partition function of quantum D3 brane wrapped on
S
1
×
S
3
in a twisted modification of the
AdS
5
×
S
5
string background, depending on the index R-symmetry fugacity. Our calculation does not exploit directly supersymmetry. It is based on the determination of the partition function of the various bosonic and fermionic fluctuations on the wrapped brane whose action is conformal with specific constant holonomies along thermal cycle. We show how those partition functions may be obtained by adapting the operator counting method of Cardy to the twisted background.
A bstract We study four-dimensional $$\mathcal{N}$$ = 2 superconformal circular, cyclic symmetric quiver theories which are planar equivalent to $$\mathcal{N}$$ = 4 super Yang-Mills. We use ...localization to compute nonplanar corrections to the free energy and the circular half-BPS Wilson loop in these theories for an arbitrary number of nodes, and examine their behaviour in the limit of long quivers. Exploiting the relationship between the localization quiver matrix integrals and an integrable Bessel operator, we find a closed-form expression for the leading nonplanar correction to both observables in the limit when the number of nodes and ’t Hooft coupling become large. We demonstrate that it has different asymptotic behaviour depending on how the two parameters are compared, and interpret this behaviour in terms of properties of a lattice model defined on the quiver diagram.
A
bstract
We consider U(
N
)
N
= 4 super Yang-Mills theory and discuss how to extract the strong coupling limit of non-planar corrections to observables involving the
1
2
-BPS Wilson loop. Our ...approach is based on a suitable saddle point treatment of the Eynard-Orantin topological recursion in the Gaussian matrix model. Working directly at strong coupling we avoid the usual procedure of first computing observables at finite planar coupling
λ
, order by order in 1
/N
, and then taking the
λ
≫ 1 limit. In the proposed approach, matrix model multi-point resolvents take a simplified form and some structures of the genus expansion, hardly visible at low order, may be identified and rigorously proved. As a sample application, we consider the expectation value of multiple coincident circular supersymmetric Wilson loops as well as their correlator with single trace chiral operators. For these quantities we provide novel results about the structure of their genus expansion at large tension, generalising recent results in
arXiv:2011.02885
.
A
bstract
Localization approach to
N
= 2 superconformal SU(
N
) × SU(
N
) quiver theory leads to a non-Gaussian two-matrix model representation for the expectation value of BPS circular SU(
N
) ...Wilson loop
W
. We study the subleading 1
/N
2
term in the large
N
expansion of
W
at weak and strong coupling. We concentrate on the case of the symmetric quiver with equal gauge couplings which is equivalent to the ℤ
2
orbifold of the SU(2
N
)
N
= 4 SYM theory. This orbifold gauge theory should be dual to type IIB superstring in AdS
5
× (
S
5
/
ℤ
2
). We present a string theory argument suggesting that the 1
/N
2
term in
W
in the orbifold theory should have the same strong-coupling asymptotics
λ
3
/
2
as in the
N
= 4 SYM case. We support this prediction on the gauge theory side by a numerical study of the localization matrix model. We also find a relation between the 1
/N
2
term in the Wilson loop expectation value and the derivative of the free energy of the orbifold gauge theory on 4-sphere.
A
bstract
We present a quantum M2 brane computation of the instanton prefactor in the leading non-perturbative contribution to the ABJM 3-sphere free energy at large
N
and fixed level
k
. Using ...supersymmetric localization, such instanton contribution was found earlier to take the form
F
inst
N
k
=
−
sin
2
2
π
k
−
1
exp
−
2
π
2
N
k
+
.
…
The exponent comes from the action of an M2 brane instanton wrapped on
S
3
/ℤ
k
, which represents the M-theory uplift of the ℂP
1
instanton in type IIA string theory on AdS
4
× ℂP
3
. The IIA string computation of the leading large
k
term in the instanton prefactor was recently performed in arXiv:2304.12340. Here we find that the exact value of the prefactor
sin
2
2
π
k
−
1
is reproduced by the 1-loop term in the M2 brane partition function expanded near the
S
3
/ℤ
k
instanton configuration. As in the Wilson loop example in arXiv:2303.15207, the quantum M2 brane computation is well defined and produces a finite result in exact agreement with localization.
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