A
bstract
We propose a method to compute the scattering angle for classical black hole scattering directly from two massive particle irreducible diagrams in a heavy-mass effective field theory ...approach to general relativity, without the need of subtracting iteration terms. The amplitudes in this effective theory are constructed using a recently proposed novel colour-kinematic/double copy for tree-level two-scalar, multi-graviton amplitudes, where the BCJ numerators are gauge invariant and local with respect to the massless gravitons. These tree amplitudes, together with graviton tree amplitudes, enter the construction of the required
D
-dimensional loop integrands and allow for a direct extraction of contributions relevant for classical physics. In particular the soft/heavy-mass expansions of full integrands is circumvented, and all iterating contributions can be dropped from the get go. We use this method to compute the scattering angle up to third post-Minkowskian order in four dimensions, including radiation reaction contributions, also providing the expression of the corresponding integrand in
D
dimensions.
A
bstract
We propose a new form of the colour-kinematics/double-copy duality for heavy-mass effective field theories, which we apply to construct compact expressions for tree amplitudes with heavy ...matter particles in Yang-Mills and in gravity to leading order in the mass. In this set-up, the new BCJ numerators are fixed uniquely and directly written in terms of field strengths, making gauge invariance manifest. Furthermore, they are local and automatically satisfy the Jacobi relations and crossing symmetry. We construct these BCJ numerators explicitly up to six particles. We also discuss relations of the BCJ numerators in the heavy-mass effective theory with those in pure Yang-Mills amplitudes.
A
bstract
This paper concerns a special class of
n
-point correlation functions of operators in the stress tensor supermultiplet of
N
= 4 supersymmetric SU(
N
) Yang-Mills theory. These are “maximal ...U(1)
Y
-violating” correlators that violate the bonus U(1)
Y
charge by a maximum of 2(
n −
4) units. We will demonstrate that such correlators satisfy SL(2
,
ℤ)-covariant recursion relations that relate
n
-point correlators to (
n −
1)-point correlators in a manner analogous to the soft dilaton relations that relate the corresponding amplitudes in flat-space type IIB superstring theory. These recursion relations are used to determine terms in the large-
N
expansion of
n
-point maximal U(1)
Y
-violating correlators in the chiral sector, including correlators with four superconformal stress tensor primaries and (
n −
4) chiral Lagrangian operators, starting from known properties of the
n
= 4 case. We concentrate on the first three orders in 1/
N
beyond the supergravity limit. The Mellin representations of the correlators are polynomials in Mellin variables, which correspond to higher derivative contact terms in the low-energy expansion of type IIB superstring theory in
AdS
5
× S
5
at the same orders as
R
4
, d
4
R
4
and
d
6
R
4
. The coupling constant dependence of these terms is found to be described by non-holomorphic modular forms with holomorphic and anti-holomorphic weights (
n −
4
,
4
− n
) that are SL(2
,
ℤ)-covariant derivatives of Eisenstein series and certain generalisations. This determines a number of non-leading contributions to U(1)
Y
-violating
n
-particle interactions (
n >
4) in the low-energy expansion of type IIB superstring amplitudes in
AdS
5
× S
5
.
A
bstract
We present a novel expression for an integrated correlation function of four superconformal primaries in SU(
N
)
N
= 4 supersymmetric Yang-Mills (
N
= 4 SYM) theory. This integrated ...correlator, which is based on supersymmetric localisation, has been the subject of several recent developments. In this paper the correlator is re-expressed as a sum over a two dimensional lattice that is valid for all
N
and all values of the complex Yang-Mills coupling
τ
=
θ
/
2
π
+
4
πi
/
g
YM
2
. In this form it is manifestly invariant under SL(2
,
ℤ) Montonen-Olive duality. Furthermore, it satisfies a remarkable Laplace-difference equation that relates the SU(
N
) correlator to the SU(
N
+ 1) and SU(
N −
1) correlators. For any fixed value of
N
the correlator can be expressed as an infinite series of non-holomorphic Eisenstein series,
E
s
τ
τ
¯
with
s
∈ ℤ, and rational coefficients that depend on the values of
N
and
s
. The perturbative expansion of the integrated correlator is an asymptotic but Borel summable series, in which the
n
-loop coefficient of order (
g
YM
/
π
)
2
n
is a rational multiple of
ζ
(2
n
+ 1). The
n
= 1 and
n
= 2 terms agree precisely with results determined directly by integrating the expressions in one-loop and two-loop perturbative
N
= 4 SYM field theory. Likewise, the charge-
k
instanton contributions (|
k
| = 1
,
2
, . . .
) have an asymptotic, but Borel summable, series of perturbative corrections. The large-
N
expansion of the correlator with fixed
τ
is a series in powers of
N
1
2
−
ℓ
(
ℓ
∈ ℤ) with coefficients that are rational sums of
E
s
τ
τ
¯
with
s
∈ ℤ + 1/2. This gives an all orders derivation of the form of the recently conjectured expansion. We further consider the ’t Hooft topological expansion of large-
N
Yang-Mills theory in which
λ
=
g
YM
2
N
is fixed. The coefficient of each order in the 1
/N
expansion can be expanded as a series of powers of
λ
that converges for
|λ| < π
2
. For large
λ
this becomes an asymptotic series when expanded in powers of
1
/
λ
with coefficients that are again rational multiples of odd zeta values, in agreement with earlier results and providing new ones. We demonstrate that the large-
λ
series is not Borel summable, and determine its resurgent non-perturbative completion, which is
O
exp
−
2
λ
.
Unifying relations for scattering amplitudes Cheung, Clifford; Shen, Chia-Hsien; Wen, Congkao
The journal of high energy physics,
02/2018, Letnik:
2018, Številka:
2
Journal Article
Recenzirano
Odprti dostop
A
bstract
We derive new amplitudes relations revealing a hidden unity among a wideranging variety of theories in arbitrary spacetime dimensions. Our results rely on a set of Lorentz invariant ...differential operators which transmute physical tree-level scattering amplitudes into new ones. By transmuting the amplitudes of gravity coupled to a dilaton and two-form, we generate all the amplitudes of Einstein-Yang-Mills theory, Dirac-Born-Infield theory, special Galileon, nonlinear sigma model, and biadjoint scalar theory. Transmutation also relates amplitudes in string theory and its variants. As a corollary, celebrated aspects of gluon and graviton scattering like color-kinematics duality, the KLT relations, and the CHY construction are inherited traits of the transmuted amplitudes. Transmutation recasts the Adler zero as a trivial consequence of the Weinberg soft theorem and implies new subleading soft theorems for certain scalar theories.
A
bstract
We present a compact formula in Mellin space for the four-point tree-level holographic correlators of chiral primary operators of arbitrary conformal weights in (2
,
0) supergravity on
AdS
...3
× S
3
, with two operators in tensor multiplet and the other two in gravity multiplet. This is achieved by solving the recursion relation arising from a hidden six-dimensional conformal symmetry. We note the compact expression is obtained after carefully analysing the analytic structures of the correlators. Various limits of the correlators are studied, including the maximally R-symmetry violating limit and flat-space limit.
A
bstract
We present a formula for the holographic 4-point correlators in AdS
3
×
S
3
involving four single-trace operators of dimension
k, k, l, l
. As an input we use the super-gravity results for ...the Heavy-Heavy-Light-Light correlators that can be derived by studying the linear fluctuations around known asymptotically AdS
3
×
S
3
geometries. When the operators of dimension
k
and
l
are in the same multiplet there are contributions due to the exchange of single-trace operators in the
t
and
u
-channels, which are not captured by the approach mentioned above. However by rewriting the
s
-channel results in Mellin space we obtain a compact expression for the
s
-channel contribution that makes it possible to conjecture a formula for the complete result. We discuss some consistency checks that our proposal meets.
A
bstract
The exact expressions for integrated maximal U(1)
Y
violating (MUV)
n
-point correlators in SU(
N
)
N
= 4 supersymmetric Yang-Mills theory are determined. The analysis generalises previous ...results on the integrated correlator of four superconformal primaries and is based on supersymmetric localisation. The integrated correlators are functions of
N
and
τ
=
θ/
(2
π
) + 4
πi/
g
YM
2
, and are expressed as two-dimensional lattice sums that are modular forms with holomorphic and anti-holomorphic weights (
w, −w
) where
w
=
n −
4. The correlators satisfy Laplace-difference equations that relate the SU(
N
+1), SU(
N
) and SU(
N−
1) expressions and generalise the equations previously found in the
w
= 0 case. The correlators can be expressed as infinite sums of Eisenstein modular forms of weight (
w, −w
). For any fixed value of
N
the perturbation expansion of this correlator is found to start at order (
g
YM
2
N
)
w
. The contributions of Yang-Mills instantons of charge
k >
0 are of the form
q
k
f
(
g
YM
), where
q
=
e
2
πiτ
and
f
(
g
YM
) =
O
(
g
YM
−
2
w
) when
g
YM
2
≪ 1. Anti-instanton contributions have charge
k <
0 and are of the form
q
¯
k
f
̂
g
YM
, where
f
̂
g
YM
=
O
g
YM
2
w
when
g
YM
2
≪ 1. Properties of the large-
N
expansion are in agreement with expectations based on the low energy expansion of flat-space type IIB superstring amplitudes. We also comment on the identification of
n
-point free-field MUV correlators with the integrands of (
n −
4)-loop perturbative contributions to the four-point correlator. In particular, we emphasise the important rôle of SL(2
,
ℤ)-covariance in the construction.
A
bstract
We study loop corrections to scattering amplitudes in the world-volume theory of a probe D3-brane, which is described by the supersymmetric Dirac-Born-Infeld theory. We show that the ...D3-brane loop superamplitudes can be obtained from the tree-level superamplitudes in the world-volume theory of a probe M5-brane (or D5-brane). The M5-brane theory describes self-interactions of an abelian tensor supermultiplet with (2
,
0) supersymmetry, and the tree-level superamplitudes are given by a twistor formula. We apply the construction to the maximally-helicity-violating (MHV) amplitudes in the D3- brane theory at one-loop order, which are purely rational terms (except for the four-point amplitude). The results are further confirmed by generalised unitarity methods. Through a supersymmetry reduction on the M5-brane tree-level superamplitudes, we also construct one-loop corrections to the non-supersymmetric D3-brane amplitudes, which agree with the known results in the literature.
A
bstract
We study the four-point function of the lowest-lying half-BPS operators in the
N
= 4 SU(
N
) super-Yang-Mills theory and its relation to the flat-space four-graviton amplitude in type IIB ...superstring theory. We work in a large-
N
expansion in which the complexified Yang-Mills coupling
τ
is fixed. In this expansion, non-perturbative instanton contributions are present, and the SL(2
,
ℤ) duality invariance of correlation functions is manifest. Our results are based on a detailed analysis of the sphere partition function of the mass-deformed SYM theory, which was previously computed using supersymmetric localization. This partition function determines a certain integrated correlator in the undeformed
N
= 4 SYM theory, which in turn constrains the four-point correlator at separated points. In a normalization where the two-point functions are proportional to
N
2
−
1 and are independent of
τ
and
τ
¯
, we find that the terms of order
N
and
1
/
N
in the large
N
expansion of the four-point correlator are proportional to the non-holomorphic Eisenstein series
E
3
2
τ
τ
¯
and
E
5
2
τ
τ
¯
, respectively. In the flat space limit, these terms match the corresponding terms in the type IIB S-matrix arising from
R
4
and
D
4
R
4
contact inter-actions, which, for the
R
4
case, represents a check of AdS/CFT at finite string coupling. Furthermore, we present striking evidence that these results generalize so that, at order
N
1
2
−
m
with integer
m ≥
0, the expansion of the integrated correlator we study is a linear sum of non-holomorphic Eisenstein series with half-integer index, which are manifestly SL(2
,
ℤ) invariant.
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