A
bstract
We study symmetry-breaking line defects in the Wilson-Fisher theory with
O
(2
N
+ 1) global symmetry near four dimensions and symmetry-preserving surface defects in a cubic model with
O
(2
...N
) global symmetry near six dimensions. We introduce a scaling limit inspired by the large charge expansion in Conformal Field Theory. Using this, we compute the beta function for the defect coupling which allows to identify the corresponding Defect Conformal Field Theories. We also compute the correlation function of two parallel defects as well as correlation functions of certain defect operators with large charge under the surviving symmetry.
A
bstract
We compute thermal 2-point correlation functions in the black brane
AdS
5
background dual to 4d CFT’s at finite temperature for operators of large scaling dimension. We find a formula that ...matches the expected structure of the OPE. It exhibits an exponentiation property, whose origin we explain. We also compute the first correction to the two-point function due to graviton emission, which encodes the proper time from the event horizon to the black hole singularity.
A
bstract
We consider defect operators in scalar field theories in dimensions
d
= 4 −
ϵ
and
d
= 6 −
ϵ
with self-interactions given by a general marginal potential. In a double scaling limit, where ...the bulk couplings go to zero and the defect couplings go to infinity, the bulk theory becomes classical and the quantum defect theory can be solved order by order in perturbation theory. We compute the defect
β
functions to two loops and study the Renormalization Group flows. The defect fixed points can move and merge, leading to fixed point annihilation; and they exhibit a remarkable factorization property where the
c
-dependence gets disentangled from the coupling dependence.
Holographic thermal correlators revisited Krishna, Hare; Rodriguez-Gomez, D.
The journal of high energy physics,
11/2021, Letnik:
2021, Številka:
11
Journal Article
Recenzirano
Odprti dostop
A
bstract
We study 2-point correlation functions for scalar operators in position space through holography including bulk cubic couplings as well as higher curvature couplings to the square of the ...Weyl tensor. We focus on scalar operators with large conformal dimensions. This allows us to use the geodesic approximation for propagators. In addition to the leading order contribution, captured by geodesics anchored at the insertion points of the operators on the boundary and probing the bulk geometry thoroughly studied in the literature, the first correction is given by a Witten diagram involving both the bulk cubic coupling and the higher curvature couplings. As a result, this correction is proportional to the VEV of a neutral operator
O
k
and thus probes the interior of the black hole exactly as in the case studied by Grinberg and Maldacena
13
. The form of the correction matches the general expectations in CFT and allows to identify the contributions of
T
n
O
k
(being
T
n
the general contraction of
n
energy-momentum tensors) to the 2-point function. This correction is actually the leading term for off-diagonal correlators (i.e. correlators for operators of different conformal dimension), which can then be computed holographically in this way.
A
bstract
We study 2-point and 3-point functions in CFT at finite temperature for large dimension operators using holography. The 2-point function leads to a universal formula for the holographic ...free energy in
d
dimensions in terms of the
c
-anomaly coefficient. By including
α
′ corrections to the black brane background, we reproduce the leading correction at strong coupling. In turn, 3-point functions have a very intricate structure, exhibiting a number of interesting properties. In simple cases, we find an analytic formula. When the dimensions satisfy ∆
i
= ∆
j
+ ∆
k
, the thermal 3-point function satisfies a factorization property. We argue that in
d >
2 factorization is a reflection of the semiclassical regime.
A
bstract
We derive exact formulas for circular Wilson loops in the
N
= 4 and
N
= 2
*
theories with gauge groups U(
N
) and SU(
N
) in the
k
-fold symmetrized product representation. The formulas ...apply in the limit of large
k
and small Yang-Mills coupling
g
, with fixed effective coupling
κ
≡
g
2
k
, and for any finite
N
. In the SU(2) and U(2) cases, closed analytic formulas are obtained for any
k
, while the 1
/k
series expansions are asymptotic. In the
N
≫ 1 limit, with
N
≪
k
, there is an overlapping regime where the formulas can be confronted with results from holography. Simple formulas for correlation functions between the
k
-symmetric Wilson loops and chiral primary operators are also given.
A
bstract
We compute general higher-point functions in the sector of large charge operators
ϕ
n
,
ϕ
¯
n
at large charge in O(2)
ϕ
¯
ϕ
2
theory. We find that there is a special class of “extremal” ...correlators having only one insertion of
ϕ
¯
n
that have a remarkably simple form in the double-scaling limit
n
→∞ at fixed
g n
2
≡ λ, where
g
~
ϵ
is the coupling at the O(2) Wilson-Fisher fixed point in 4 −
ϵ
dimensions. In this limit, also non-extremal correlators can be computed. As an example, we give the complete formula for
ϕ
x
1
n
ϕ
x
2
n
ϕ
¯
x
3
n
ϕ
¯
x
4
n
, which reveals an interesting structure.
A
bstract
We investigate defects in scalar field theories in four and six dimensions in a double-scaling (semiclassical) limit, where bulk loops are suppressed and quantum effects come from the ...defect coupling. We compute
β
-functions up to four loops and find that fixed points satisfy dimensional disentanglement — i.e. their dependence on the space dimension is factorized from the coupling dependence — and discuss some physical implications. We also give an alternative derivation of the
β
functions by computing systematic logarithmic corrections to the Coulomb potential. In this natural scheme,
β
functions turn out to be a gradient of a ‘Hamiltonian’ function
H
. We also obtain closed formulas for the dimension of scalar operators and show that instabilities do not occur for potentials bounded from below. The same formulas are reproduced using Rigid Holography.
A
bstract
We study the sector of large charge operators
ϕ
n
(
ϕ
being the complexified scalar field) in the
O
(2) Wilson-Fisher fixed point in 4
−E
dimensions that emerges when the coupling takes the ...critical value
g ∼
𝜖. We show that, in the limit
g →
0, when the theory naively approaches the gaussian fixed point, the sector of operators with
n → ∞
at fixed
g n
2
≡ λ
remains non-trivial. Surprisingly, one can compute the exact 2-point function and thereby the non-trivial anomalous dimension of the operator
ϕ
n
by a full resummation of Feynman diagrams. The same result can be reproduced from a saddle point approximation to the path integral, which partly explains the existence of the limit. Finally, we extend these results to the three-dimensional
O
(2)-symmetric theory with (
ϕ
¯
ϕ
)
3
potential.
A
bstract
We study large charge sectors in the O(
N
) model in 6
− ϵ
dimensions. For 4
< d <
6, in perturbation theory, the quartic O(
N
) theory has a UV stable fixed point at large
N
. It was ...recently argued that this fixed point can be described in terms of an IR fixed point of a cubic O(
N
) model. By considering a double scaling limit of large charge and weak couplings, we compute two-point and all “extremal” higher-point correlation functions for large charge operators and find a precise equivalence between both pictures. Instanton instabilities are found to be exponentially suppressed at large charge. We also consider correlation function of U(1)-invariant meson operators in the O(2
N
) ⊃ U(1) × SU(
N
) theory, as a first step towards tests of (higher spin) AdS
/
CFT.
PDF