47 research outputs found
MHV amplitudes at strong coupling and linearized TBA equations
The maximally helicity violating (MHV) amplitudes of super
Yang-Mills theory at strong coupling are obtained by solving auxiliary
thermodynamic Bethe ansatz (TBA) integral equations. We consider a limit where
the TBA equations are linearized for large chemical potentials and masses
therein. By solving the linearized equations, we derive analytic expansions of
the 6-point MHV amplitudes in terms of the ratio of the chemical potential
and the mass . The expansions are valid up to corrections exponentially
small in or inversely proportional to powers of . The analytic
expansions describe the amplitudes for small conformal cross-ratios of the
particle momenta in a standard basis, and interpolate the amplitudes with equal
cross-ratios and those in soft/collinear limits. The leading power corrections
are also obtained analytically. We compare the 6-point rescaled remainder
functions at strong coupling and at 2 loops for the above kinematics. They are
rather different, in contrast to other kinematic regions discussed in the
literature where they are found to be similar to each other.Comment: 41 pages, 9 figures; (v2) a reference added, typos corrected, minor
revision
Quantum Wronskian approach to six-point gluon scattering amplitudes at strong coupling
We study the six-point gluon scattering amplitudes in N=4 super Yang-Mills
theory at strong coupling based on the twisted Z_4-symmetric integrable model.
The lattice regularization allows us to derive the associated thermodynamic
Bethe ansatz (TBA) equations as well as the functional relations among the
Q-/T-/Y-functions. The quantum Wronskian relation for the Q-/T-functions plays
an important role in determining a series of the expansion coefficients of the
T-/Y-functions around the UV limit, including the dependence on the twist
parameter. Studying the CFT limit of the TBA equations, we derive the leading
analytic expansion of the remainder function for the general kinematics around
the limit where the dual Wilson loops become regular-polygonal. We also compare
the rescaled remainder functions at strong coupling with those at two, three
and four loops, and find that they are close to each other along the
trajectories parameterized by the scale parameter of the integrable model.Comment: 30 pages, 8 figures; (v2) a reference adde
On the mass-coupling relation of multi-scale quantum integrable models
We determine exactly the mass-coupling relation for the simplest multi-scale
quantum integrable model, the homogenous sine-Gordon model with two independent
mass-scales. We first reformulate its perturbed coset CFT description in terms
of the perturbation of a projected product of minimal models. This
representation enables us to identify conserved tensor currents on the UV side.
These UV operators are then mapped via form factor perturbation theory to
operators on the IR side, which are characterized by their form factors. The
relation between the UV and IR operators is given in terms of the sought-for
mass-coupling relation. By generalizing the sum rule Ward identity we
are able to derive differential equations for the mass-coupling relation, which
we solve in terms of hypergeometric functions. We check these results against
the data obtained by numerically solving the thermodynamic Bethe Ansatz
equations, and find a complete agreement.Comment: 55 pages, 9 figures, reference added, minor changes, published
versio
Exact mass-coupling relation for the homogeneous sine-Gordon model
We derive the exact mass-coupling relation of the simplest multi-scale
quantum integrable model, i.e., the homogeneous sine-Gordon model with two mass
scales. The relation is obtained by comparing the perturbed conformal field
theory description of the model valid at short distances to the large distance
bootstrap description based on the model's integrability. In particular, we
find a differential equation for the relation by constructing conserved tensor
currents which satisfy a generalization of the sum rule Ward identity.
The mass-coupling relation is written in terms of hypergeometric functions.Comment: 6 pages, 2 figures. (v2) references and clarifications added;
original title "Exact mass-coupling relation of the simplest multi-scale
quantum integrable model" changed for journa
g-Functions and gluon scattering amplitudes at strong coupling
We study gluon scattering amplitudes/Wilson loops in N=4 super Yang-Mills
theory at strong coupling by calculating the area of the minimal surfaces in
AdS_3 based on the associated thermodynamic Bethe ansatz system. The remainder
function of the amplitudes is computed by evaluating the free energy, the T-
and Y-functions of the homogeneous sine-Gordon model. Using conformal field
theory (CFT) perturbation, we examine the mass corrections to the free energy
around the CFT point corresponding to the regular polygonal Wilson loop. Based
on the equivalence between the T-functions and the g-functions, which measure
the boundary entropy, we calculate corrections to the T- and Y-functions as
well as express them at the CFT point by the modular S-matrix. We evaluate the
remainder function around the CFT point for 8 and 10-point amplitudes
explicitly and compare these analytic expressions with the 2-loop formulas. The
two rescaled remainder functions show very similar power series structures.Comment: 51 pages, 4 figures, v2: some comments and references added, based on
the published version, v3: minor change
Thermodynamic Bethe Ansatz Equations for Minimal Surfaces in AdS_3
We study classical open string solutions with a null polygonal boundary in
AdS_3 in relation to gluon scattering amplitudes in N=4 super Yang-Mills at
strong coupling. We derive in full detail the set of integral equations
governing the decagonal and the dodecagonal solutions and identify them with
the thermodynamic Bethe ansatz equations of the homogeneous sine-Gordon models.
By evaluating the free energy in the conformal limit we compute the central
charges, from which we observe general correspondence between the polygonal
solutions in AdS_n and generalized parafermions.Comment: 25 pages, 4 figures, v2: a figure and references added, minor
corrections, v3: references added, minor corrections, to appear in JHE
Elevated plasma CXCL12 alpha is associated with a poorer prognosis in pulmonary arterial hypertension.
Recent work in preclinical models suggests that signalling via the pro-angiogenic and proinflammatory
cytokine, CXCL12 (SDF-1), plays an important pathogenic role in pulmonary
hypertension (PH). The objective of this study was to establish whether circulating concentrations
of CXCL12α were elevated in patients with PAH and related to mortalit
T-functions and multi-gluon scattering amplitudes
We study gluon scattering amplitudes/Wilson loops in N=4 super Yang-Mills
theory at strong coupling which correspond to minimal surfaces with a
light-like polygonal boundary in AdS_3. We find a concise expression of the
remainder function in terms of the T-function of the associated thermodynamic
Bethe ansatz (TBA) system. Continuing our previous work on the analytic
expansion around the CFT/regular-polygonal limit, we derive a formula of the
leading-order expansion for the general 2n-point remainder function. The
T-system allows us to encode its momentum dependence in only one function of
the TBA mass parameters, which is obtained by conformal perturbation theory. We
compute its explicit form in the single mass cases. We also find that the
rescaled remainder functions at strong coupling and at two loops are close to
each other, and their ratio at the leading order approaches a constant near 0.9
for large n.Comment: 36 pages, 5 figures, v2: published version, v3: minor correction