121785638
Twist symmetry and open string Wilson lines
Abstract The Mobius amplitude plays an important role in open-string theories, since it determines which sectors of a given model consist of unoriented open strings. It also fixes the Chan-Paton representations of all their states, according to the behavior under the interchange of the ends of open strings (“twist”). In this paper we discuss the role played by conventional Wilson lines in Chan-Paton symmetry breaking, and we show that the presence of an extended symmetry algebra allows, in general, a number of choices for the behavior of massive states under twist. This freedom may be ascribed to additional discrete Wilson lines, and yields consistent modifications of the group assignments, that are illustrated in a number of examples.
14121046
Holographic three-point functions: one step beyond the tradition
Abstract Within the program of holographic renormalization, we discuss the computation of three-point correlation functions along RG flows. We illustrate the procedure in two simple cases. In an RG flow to the Coulomb branch of N =4 SYM theory we derive a compact and finite expression for the three-point function of lowest CPOs dual to inert scalars. In the GPPZ flow, that captures some features of N =1 SYM theory, we identify two new logarithmically divergent counterterms and compute the three-point function with insertion of two inert scalars and one active scalar that mixes with the stress tensor. By amputating the external legs at the mass poles we extract the finite and scheme independent trilinear couplings of the corresponding superglueballs. Finally we outline the procedure for computing three-point functions with insertions of the stress tensor as well as of (broken) R-symmetry currents.
16024712
Twelve-dimensional aspects of four-dimensional N = 1 type I vacua
Abstract Four-dimensional supergravity theories are reinterpreted in a 12-dimensional F-theory framework. The O(8) symmetry of N = 8 supergravity is related to a reduction of F-theory on T8, with the seventy scalars formally associated, by O(8) triality, to a fully compactified four-form A4. For the N = 1 type I model recently obtained from the type IIB string on the Z orbifold, we identify the Kahler manifold of the untwisted scalars in the unoriented closed sector with the generalized Siegel upper-half plane Sp(8, R) (SU(4) × U(1)) . The SU(4) factor reflects the holonomy group of Calabi-Yau four-folds.
7025247
Discrete torsion in non-geometric orbifolds and their open-string descendants
Abstract We discuss some Z N L × Z N R orbifold compactifications of the type IIB superstring to D =4,6 dimensions and their type I descendants. Although the Z N L × Z N R generators act asymmetrically on the chiral string modes, they result into left–right symmetric models that admit sensible unorientable reductions. We carefully work out the phases that appear in the modular transformations of the chiral amplitudes and identify the possibility of introducing discrete torsion. We propose a simplifying ansatz for the construction of the open-string descendants in which the transverse-channel Klein-bottle, annulus and Mobius-strip amplitudes are numerically identical in the proper parametrization of the world-sheet. A simple variant of the ansatz for the Z 2 L × Z 2 R orbifold gives rise to models with supersymmetry breaking in the open-string sector.
15907576
Non-perturbative and flux superpotentials for type I strings on the Z3 orbifold
Abstract Non-perturbative effects are studied for type I strings on the Z 3 orbifold with Chan–Paton symmetry broken by Wilson lines. Generalizing previous analyses that have focussed on (bi)fundamentals, it is argued that (anti)symmetric representations of the resulting gauge group play a decisive role in generating an ADS-like superpotential in this and related cases. Non-perturbative corrections in the closed string moduli are only allowed if properly dressed with open string fields charged under the anomalous U ( 1 ) of the orbifold. A general discussion of instanton effects in SYM and string theories is given. Non-perturbative superpotentials induced by both ED5's and ED1's are analyzed. The superpotential generated by closed string fluxes, viz. Scherk–Schwarz shifts (torsion), R–R 3-form flux as well as non-geometric fluxes is derived. Some preliminary comments on the compatibility of the two kinds of superpotentials and the issue of moduli stabilization are presented.
119040998
Instanton Effects in Supersymmetric Yang-Mills Theories on ALE Gravitational Backgrounds
In this letter we report on the computation of instanton-dominated correlation functions in supersymmetric YM theories on ALE spaces. Following the approach of Kronheimer and Nakajima, we explicitly construct the self-dual connection on ALE spaces necessary to perform such computations. We restrict our attention to the simplest case of an $SU(2)$ connection with lowest Chern class on the Eguchi-Hanson gravitational background.
119243475
Light-like Wilson loops in ABJM and maximal transcendentality
A bstractWe revisit the computation of the two-loop light-like tetragonal Wilson loop for three dimensional pure Chern-Simons and $ \mathcal{N} $= 6 Chern-Simons-matter theory, within dimensional regularization with dimensional reduction scheme. Our examination shows that, contrary to prior belief, the result respects maximal transcendentality as is the case of the four-point scattering amplitude of the theory. Interestingly, the corrected result matches exactly the scattering amplitude both in the divergent and in the finite parts, constants included.
119238771
Scattering in ABJ theories
A bstractWe study the correspondence between scattering amplitudes and Wilson loops in three-dimensional Chern-Simons matter theories. In particular, using $ \mathcal{N} = {2} $ superspace formalism, we compute at one loop the whole spectrum of four-point superamplitudes for generic $ \mathcal{N} \geqslant {2} $ supersymmetric theories and find a vanishing result for $ \mathcal{N} = {6} $ ABJ(M) and $ \mathcal{N} = {8} $ BLG models. This restricts the possible range of theories for which Wilson loops/scattering amplitudes duality might work. At two loops, we present the computation of the four-point ABJ scattering amplitude for external chiral superfields. Extending the known result for the ABJM Wilson loop to the ABJ case we find perfect agreement. We also discuss the dual conformal invariance of our results and the relationship between the Feynman diagram computation and unitarity methods. While for the ABJM theory dual conformally invariant integrals exactly reproduce the amplitude, for the ABJ case this happens only up to a residual constant depending on the parity-violating parameter. Finally we propose a BDS-like exponentiation for the amplitude based on an analogy with the four dimensional $ \mathcal{N} = {4} $ SYM case, and discuss its strong coupling dual counterpart.
52023598
On the ABJM four-point amplitude at three loops and BDS exponentiation
A bstractWe study the three-loop four-point amplitude in ABJM theory. We determine the dual conformal invariant integrals with highest number of propagators and fix their coefficients by two-particle cuts. Evaluating such a combination of integrals in dimensional regularization we provide evidence for exponentiation of the amplitude, including the finite terms. In addition we show that the three-loop amplitude can be expressed in terms of classical polylogarithms of uniform degree of transcendentality.
102332810
Scattering amplitudes/Wilson loop duality in ABJM theory
A bstractFor $$ \mathcal{N} = 6 $$ superconformal Chern-Simons-matter theories in three dimensions, by a direct superspace Feynman diagram approach, we compute the two-loop four-point scattering amplitude with external chiral matter fields. We find that the result is in perfect agreement with the two-loop result for a light-like four-polygon Wilson loop. This is the first non-trivial evidence that an amplitudes/Wilson loop duality might work in three dimensions. Moreover, both the IR divergent and the finite parts of our two-loop result agree with a BDS-like ansatz for all-loop amplitudes where the scaling function is given in terms of the $$ \mathcal{N} = 4 $$ SYM one, according to the conjectured Bethe equations for ABJM. Consequently, we are able to make a prediction for the four-loop correction to the amplitude. We also discuss the dual conformal invariance of the two-loop result.
56038769
BPS Wilson loops and Bremsstrahlung function in ABJ(M): a two loop analysis
A bstractWe study a family of circular BPS Wilson loops in $ \mathcal{N} $ = 6 super Chern-Simons-matter theories, generalizing the usual 1/2-BPS circle. The scalar and fermionic couplings depend on two deformation parameters and these operators can be considered as the ABJ(M) counterpart of the DGRT latitudes defined in $ \mathcal{N} $ = 4 SYM. We perform a complete two-loop analysis of their vacuum expectation value, discuss the appearance of framing-like phases and propose a general relation with cohomologically equivalent bosonic operators. We make an all-loop proposal for computing the Bremsstrahlung function associated to the 1/2-BPS cusp in terms of these generalized Wilson loops. When applied to our two-loop result it reproduces the known expression. Finally, we comment on the generalization of this proposal to the bosonic 1/6-BPS case.