A
bstract
We study monopole operators with the lowest possible topological charge
q
= 1/2 at the infrared fixed point of scalar electrodynamics in 2 + 1 dimension (scalar QED
3
) with
N
complex ...scalars and Chern-Simons coupling
|k|
=
N
. In the large
N
expansion, monopole operators in this theory with spins
ℓ
<
O
N
and associated flavor representations are expected to have the same scaling dimension to sub-leading order in 1/
N
. We use the state-operator correspondence to calculate the scaling dimension to sub-leading order with the result
N −
0
.
2743 +
O
(1/
N
), which improves on existing leading order results. We also compute the
ℓ
2
/
N
term that breaks the degeneracy to sub-leading order for monopoles with spins
ℓ
=
O
N
.
A
bstract
We derive exact relations between certain integrals of the conserved flavor current four point function in 4d
N
= 2 conformal field theories (CFTs) and derivatives of the mass deformed ...sphere free energy, which can be computed exactly for gauge theories using supersymmetric localization. For conformal gauge theories with flavor groups of rank greater than one, there are at least two such integrated constraints, which can then be combined with the numerical conformal bootstrap to bound CFT data as a function of the complexified gauge coupling
τ
. We apply this strategy to the case of SU(2) conformal SQCD with flavor group SO(8), where we compute bounds on unprotected scaling dimensions as a function of
τ
that match the free theory limit, and exhibit the expected mixing between the action of the SL(2
,
ℤ) duality group and SO(8) triality.
A
bstract
We consider the four-point function of the lowest scalar in the stress-energy tensor multiplet in
N
=
8
ABJ(M) theory
1
,
2
. At large central charge
c
T
∼
N
3/2
, this correlator is given ...by the corresponding holographic correlation function in 11d supergravity on
AdS
4
×
S
7
. We use Mellin space techniques to compute the leading 1
/c
T
correction to anomalous dimensions and OPE coefficients of operators that appear in this holographic correlator. For half and quarter-BPS operators, we find exact agreement with previously computed localization results. For the other BPS and non-BPS operators, our results match the
N
=
8
numerical bootstrap for ABJ(M) at large
c
T
, which provides a precise check of unprotected observables in AdS/CFT.
A
bstract
We develop new tools for isolating CFTs using the numerical bootstrap. A “cutting surface” algorithm for scanning OPE coefficients makes it possible to find islands in high-dimensional ...spaces. Together with recent progress in large-scale semidefinite programming, this enables bootstrap studies of much larger systems of correlation functions than was previously practical. We apply these methods to correlation functions of charge-0, 1, and 2 scalars in the 3d O(2) model, computing new precise values for scaling dimensions and OPE coefficients in this theory. Our new determinations of scaling dimensions are consistent with and improve upon existing Monte Carlo simulations, sharpening the existing decades-old 8
σ
discrepancy between theory and experiment.
A
bstract
When the SU(
N
)
N
= 4 super-Yang-Mills (SYM) theory with complexified gauge coupling
τ
is placed on a round four-sphere and deformed by an
N
= 2-preserving mass parameter
m
, its free ...energy
F
(
m, τ,
τ
¯
) can be computed exactly using supersymmetric localization. In this work, we derive a new exact relation between the fourth derivative
∂
m
4
F
m
τ
τ
¯
m
=
0
of the sphere free energy and the integrated stress-tensor multiplet four-point function in the
N
= 4 SYM theory. We then apply this exact relation, along with various other constraints derived in previous work (coming from analytic bootstrap, the mixed derivative
∂
τ
∂
τ
¯
∂
m
2
F
m
τ
τ
¯
m
=
0
, and type IIB superstring theory scattering amplitudes) to determine various perturbative terms in the large
N
and large ’t Hooft coupling
λ
expansion of the
N
= 4 SYM correlator at separated points. In particular, we determine the leading large-
λ
term in the
N
= 4 SYM correlation function at order 1
/N
8
. This is three orders beyond the planar limit.
A
bstract
We compute 1
/λ
corrections to the four-point functions of half-BPS operators in SU(
N
)
N
= 4 super-Yang-Mills theory at large
N
and large ’t Hooft coupling
λ
=
g
YM
2
N
using two methods. ...Firstly, we relate integrals of these correlators to derivatives of the mass deformed
S
4
free energy, which was computed at leading order in large
N
and to all orders in 1
/λ
using supersymmetric localization. Secondly, we use AdS/CFT to relate these 1
/λ
corrections to higher derivative corrections to supergravity for scattering amplitudes of Kaluza-Klein scalars in IIB string theory on AdS
5
× S
5
, which in the flat space limit are known from worldsheet calculations. These two methods match at the order corresponding to the tree level
R
4
interaction in string theory, which provides a precise check of AdS/CFT beyond supergravity, and allow us to derive the holographic correlators to tree level
D
4
R
4
order. Combined with constraints from 1, our results can be used to derive CFT data to one-loop
D
4
R
4
order. Finally, we use AdS/CFT to fix these correlators in the limit where
N
is taken to be large while
g
YM is kept fixed. In this limit, we present a conjecture for the small mass limit of the
S
4
partition function that includes all instanton corrections and is written in terms of the same Eisenstein series that appear in the study of string theory scattering amplitudes.
A
bstract
We show that by studying the flat spacetime limit of the Mellin amplitude associated with the four-point correlation function of scalar operators in the stress tensor multiplet of ABJM ...theory, one can produce the momentum expansion of the M-theory four-graviton S-matrix elements. Using CFT data previously obtained from the supersymmetric localization method, we carry out this procedure explicitly to the second nontrivial order in the momentum expansion, and recover precisely the known
R
4
contribution to the scattering amplitude of super-gravitons in M-theory in eleven dimensions.
The M-theory archipelago Agmon, Nathan B.; Chester, Shai M.; Pufu, Silviu S.
The journal of high energy physics,
02/2020, Volume:
2020, Issue:
2
Journal Article
Peer reviewed
Open access
A
bstract
We combine supersymmetric localization results and the numerical conformal bootstrap technique to study the 3d maximally supersymmetric (
N
= 8) CFT on
N
coincident M2-branes (the U(
N
)
k
...× U(
N
)
−k
ABJM theory at Chern-Simons level
k
= 1). In particular, we perform a mixed correlator bootstrap study of the superconformal primaries of the stress tensor multiplet and of the next possible lowest-dimension half-BPS multiplet that is allowed by 3d
N
= 8 superconformal symmetry. Of all known 3d
N
= 8 SCFTs, the
k
= 1 ABJM theory is the only one that contains both types of multiplets in its operator spectrum. By imposing the values of the short OPE coefficients that can be computed exactly using supersymmetric localization, we are able to derive precise islands in the space of semi-short OPE coefficients for an infinite number of such coefficients. We find that these islands decrease in size with increasing
N
. More generally, we also analyze 3d
N
= 8 SCFT that contain both aforementioned multiplets in their operator spectra without inputing any additional information that is specific to ABJM theory. For such theories, we compute upper and lower bounds on the semi-short OPE coefficients as well as upper bounds on the scaling dimension of the lowest unprotected scalar operator. These latter bounds are more constraining than the analogous bounds previously derived from a single correlator bootstrap of the stress tensor multiplet. This leads us to conjecture that the U(
N
)
2
× U(
N
+ 1)
−
2
ABJ theory, and not the
k
= 1 ABJM theory, saturates the single correlator bounds.
AdS4/CFT3 from weak to strong string coupling Binder, Damon J.; Chester, Shai M.; Pufu, Silviu S.
The journal of high energy physics,
01/2020, Volume:
2020, Issue:
1
Journal Article
Peer reviewed
Open access
A
bstract
We consider the four-point function of operators in the stress tensor multiplet of the U(
N
)
k
×
U(
N
)
−k
ABJM theory, in the limit where
N
is taken to infinity while
N/k
5
is held fixed. ...In this limit, ABJM theory is holographically dual to type IIA string theory on AdS
4
×
ℂℙ
3
at finite string coupling
g
s
∼
(
N/k
5
)
1
/
4
. While at leading order in 1
/N
, the stress tensor multiplet four-point function can be computed from type IIA supergravity, in this work we focus on the first subleading correction, which comes from tree level Witten diagrams with an
R
4
interaction vertex. Using superconformal Ward identities, bulk locality, and the mass deformed sphere free energy previously computed to all orders in 1
/N
from supersymmetric localization, we determine this
R
4
correction as a function of
N/k
5
. Taking its flat space limit, we recover the known
R
4
contribution to the type IIA S-matrix and reproduce the fact that it only receives perturbative contributions in
g
s
from genus zero and genus one string worldsheets. This is the first check of AdS/CFT at finite
g
s
for local operators. Our result for the four-point correlator interpolates between the large
N
, large ’t Hooft coupling limit and the large
N
finite
k
limit. From the bulk perspective, this is an interpolation between type IIA string theory on AdS
4
×
ℂℙ
3
at small string coupling and M-theory on AdS
4
× S
7
/
ℤ
k
.
A derivation of AdS/CFT for vector models Aharony, Ofer; Chester, Shai M.; Urbach, Erez Y.
The journal of high energy physics,
03/2021, Volume:
2021, Issue:
3
Journal Article
Peer reviewed
Open access
A
bstract
We explicitly rewrite the path integral for the free or critical
O
(
N
) (or U(
N
)) bosonic vector models in
d
space-time dimensions as a path integral over fields (including massless ...high-spin fields) living on (
d
+ 1)-dimensional anti-de Sitter space. Inspired by de Mello Koch, Jevicki, Suzuki and Yoon and earlier work, we first rewrite the vector models in terms of bi-local fields, then expand these fields in eigenmodes of the conformal group, and finally map these eigenmodes to those of fields on anti-de Sitter space. Our results provide an explicit (non-local) action for a high-spin theory on anti-de Sitter space, which is presumably equivalent in the large
N
limit to Vasiliev’s classical high-spin gravity theory (with some specific gauge-fixing to a fixed background), but which can be used also for loop computations. Our mapping is explicit within the 1
/N
expansion, but in principle can be extended also to finite
N
theories, where extra constraints on products of bulk fields need to be taken into account.
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