arXiv subjects
Publications and source records attributed to Silvia Penati.
I review recent results concerning the construction of generalised "latitude" Wilson loops in ABJM theory. In particular, the parametric Matrix Model determining these operators exactly is presented, as well as the exact prescription for computing different types of Bremsstrahlung functions from circular Wilson loops. In this context the physical meaning of framing in non-topological three-dimensional theories is clarified.
This is a compact review of recent results on supersymmetric Wilson loops in ABJ(M) and related theories. It aims to be a quick introduction to the state of the art in the field and a discussion of open problems. It is divided into short chapters devoted to different questions and techniques. Some new results, perspectives and speculations are also presented. We hope this might serve as a baseline for further studies of this topic.
We consider a Galilean N=2 supersymmetric theory in 2+1 dimensions with F-term couplings, obtained by null reduction of a relativistic Wess-Zumino model. We compute quantum corrections and we check that, as for the relativistic parent theory, the F-term does not receive quantum corrections. Even more, we find evidence that the causal structure of the non-relativistic dynamics together with particle number conservation constrain the theory to be one-loop exact.
We study quantum integrability of affine Toda theories with a line of defect. In particular, we focus on the problem of constructing quantum higher-spin conserved currents in models defined by two A_r^{(1)} Toda theories separated by a non-trivial type-I defect. For a suitable choice of the defect potential these theories are known to be classically integrable, that is they possess an infinite set of higher-spin conserved charges in involution. Studying the corresponding conservation laws at quantum level we discover that anomalies arise, which we compute exactly at all orders in the coupling constant. While for the stress-energy tensor these anomalies can be cancelled by a finite renormalization of the defect potential, we find that from the first non-trivial higher-spin current this is no longer possible. This opens the question whether these theories are indeed integrable at quantum level.
For $SU(N)$ superconformal QCD we perform a three-loop calculation of the generalized cusp anomalous dimension of the BPS Wilson loop operator using HQET formalism. We obtain an expression which is valid at generic geometric and internal angles and finite gauge group rank $N$. For equal and opposite angles this expression vanishes, proving that at these points the cusp becomes BPS. From its small angle expansion we derive the corresponding Bremsstrahlung function at three loops, matching the matrix model prediction given in terms of derivatives of the Wilson loop on the ellipsoid. Finally, we discuss possible scenarios at higher loops, with respect to the existence of a universal effective coupling in an integrable subsector of the model.
In ABJ(M) theory, we propose a matrix model for the exact evaluation of BPS Wilson loops on a latitude circular contour, so providing a new weak-strong interpolation tool. Intriguingly, the matrix model turns out to be a particular case of that computing torus knot invariants in $U(N_1|N_2)$ Chern-Simons theory. At weak coupling we check our proposal against a three-loop computation, performed for generic framing, winding number and representation. The matrix model is amenable of a Fermi gas formulation, which we use to systematically compute the strong coupling and genus expansions. For the fermionic Wilson loop the leading planar behavior agrees with a previous string theory prediction. For the bosonic operator our result provides a clue for finding the corresponding string dual configuration. Our matrix model is consistent with recent proposals for computing Bremsstrahlung functions exactly in terms of latitude Wilson loops. As a by-product, we extend the conjecture for the exact $B^θ_{1/6}$ Bremsstrahlung function to generic representations and test it with a four-loop perturbative computation. Finally, we propose an exact prediction for $B_{1/2}$ at unequal gauge group ranks.
In $\mathcal N \geq 2$ superconformal Chern-Simons-matter theories we construct the infinite family of Bogomol'nyi-Prasad-Sommerfield (BPS) Wilson loops featured by constant parametric couplings to scalar and fermion matter, including both line Wilson loops in Minkowski spacetime and circle Wilson loops in Euclidean space. We find that the connection of the most general BPS Wilson loop cannot be decomposed in terms of double-node connections. Moreover, if the quiver contains triangles, it cannot be interpreted as a supermatrix inside a superalgebra. However, for particular choices of the parameters it reduces to the well-known connections of 1/6 BPS Wilson loops in Aharony-Bergman-Jafferis-Maldacena (ABJM) theory and 1/4 BPS Wilson loops in $\mathcal N = 4$ orbifold ABJM theory. In the particular case of $\mathcal N = 2$ orbifold ABJM theory we identify the gravity duals of a subset of operators. We investigate the cohomological equivalence of fermionic and bosonic BPS Wilson loops at quantum level by studying their expectation values, and find strong evidence that the cohomological equivalence holds quantum mechanically, at framing one. Finally, we discuss a stronger formulation of the cohomological equivalence, which implies non-trivial identities for correlation functions of composite operators in the defect CFT defined on the Wilson contour and allows to make novel predictions on the corresponding unknown integrals that call for a confirmation.
We construct new families of 1/4 BPS Wilson loops in circular quiver $\mathcal N=4$ superconformal Chern-Simons-matter (SCSM) theories in three dimensions. They are defined as the holonomy of superconnections that contain non-trivial couplings to scalar and fermions, and cannot be reduced to block-diagonal matrices. Consequently, the new operators cannot be written in terms of double-node Wilson loops, as the ones considered so far in the literature. For particular values of the couplings the superconnection becomes block-diagonal and we recover the known fermionic 1/4 and 1/2 BPS Wilson loops. The new operators are cohomologically equivalent to bosonic 1/4 BPS Wilson loops and are then amenable of exact evaluation via localization techniques. Moreover, in the case of orbifold ABJM theory we identify the corresponding gravity duals for some of the 1/4 and 1/2 BPS Wilson loops.
For three-dimensional ABJ(M) theories and $\mathcal N=4$ Chern-Simons-matter quiver theories, we construct two sets of 1/2 BPS Wilson loop operators by applying the Higgsing procedure along independent directions of the moduli space, and choosing different massive modes. For theories whose dual M-theory description is known, we also determine the corresponding spectrum of 1/2 BPS M2-brane solutions. We identify the supercharges in M-theory and field theory, as well as the supercharges preserved by M2-/anti-M2-branes and 1/2 BPS Wilson loops. In particular, in $\mathcal N=4$ orbifold ABJM theory we find pairs of different 1/2 BPS Wilson loops that preserve exactly the same set of supercharges. In field theory they arise by Higgsing with the choice of either particles or antiparticles, whereas in the dual description they correspond to a pair of M2-/anti-M2-branes localized at different positions in the compact space. This result enlightens the origin of classical Wilson loop degeneracy in these theories, already discussed in arXiv:1506.07614. A discussion on possible scenarios that emerge by comparison with localization results is included.
We derive a geometric formulation of the 2d central charge $c_r$ from infinite families of 4d $\mathcal{N}=1$ superconformal field theories topologically twisted on constant curvature Riemann surfaces. They correspond to toric quiver gauge theories and are associated to D3 branes probing five dimensional Sasaki-Einstein geometries in the AdS/CFT correspondence. We show that $c_r$ can be expressed in terms of the areas of the toric diagram describing the moduli space of the 4d theory, both for toric geometries with smooth and singular horizons. We also study the relation between a-maximization in 4d and c-extremization in 2d, giving further evidences of the mixing of the baryonic symmetries with the exact R-current in two dimensions.
We present the three-loop calculation of the Bremsstrahlung function associated to the 1/2-BPS cusp in ABJM theory, including color subleading corrections. Using the BPS condition we reduce the computation to that of a cusp with vanishing angle. We work within the framework of heavy quark effective theory (HQET) that further simplifies the analytic evaluation of the relevant cusp anomalous dimension in the near-BPS limit. The result passes nontrivial tests, such as exponentiation, and is in agreement with the conjecture made in [1] for the exact expression of the Bremsstrahlung function, based on the relation with fermionic latitude Wilson loops.
Within the framework of four dimensional conformal supergravity we consider $\mathcal{N}=1,2,3,4$ supersymmetric theories generally twisted along the abelian subgroups of the R-symmetry and possibly other global symmetry groups. Upon compactification on constant curvature Riemann surfaces with arbitrary genus we provide an extensive classification of the resulting two dimensional theories according to the amount of supersymmetry that is preserved. Exploiting the c-extremization prescription introduced in arXiv:1211.4030 we develop a general procedure to obtain the central charge for 2d $\mathcal{N}=(0,2)$ theories and the expression of the corresponding R-current in terms of the original 4d one and its mixing with the other abelian global currents.
Supersymmetric localization provides exact results that should match QFT computations in some regularization scheme. The agreement is particularly subtle in three dimensions where complex answers from localization procedure sometimes arise. We investigate this problem by studying the expectation value of the 1/6 BPS Wilson loop in planar ABJ(M) theory at three loops in perturbation theory. We reproduce the corresponding term in the localization result and argue that it originates entirely from a non-trivial framing of the circular contour. Contrary to pure Chern-Simons theory, we point out that for ABJ(M) the framing phase is a non-trivial function of the couplings and that it potentially receives contributions from vertex-like diagrams. Finally, we briefly discuss the intimate link between the exact framing factor and the Bremsstrahlung function of the 1/2-BPS cusp.
In three dimensional ${\cal N}=4$ Chern-Simons-matter theories two independent fermionic Wilson loop operators can be defined, which preserve half of the supersymmetry charges and are cohomologically equivalent at classical level. We compute their three-loop expectation value in a convenient color sector and prove that the degeneracy is uplifted by quantum corrections. We expand the matrix model prediction in the same regime and by comparison we conclude that the quantum 1/2 BPS Wilson loop is the average of the two operators. We provide an all-loop argument to support this claim at any order. As a by-product, we identify the localization result at three loops as a correction to the framing factor induced by matter interactions. Finally, we comment on the quantum properties of the non-1/2 BPS Wilson loop operator defined as the difference of the two fermionic ones.
We verify the self-duality of Green-Schwarz supercoset sigma models on AdS$_d \times S^d $ backgrounds (d=2,3,5) under combined bosonic and fermionic T-dualities without gauge fixing kappa symmetry. We also prove this property for superstrings on AdS$_d \times S^d \times S^d$ (d=2,3) described by supercoset sigma models with the isometries governed by the exceptional Lie supergroups $D(2,1;α)$ (d=2) and $D(2,1;α)\times D(2,1;α)$ (d=3), which requires an additional T-dualisation along one of the spheres. Then, by taking into account the contribution of non-supercoset fermionic modes (up to the second order), we provide evidence for the T-self-duality of the complete type IIA and IIB Green-Schwarz superstring theory on AdS$_d\times S^d \times T^{10-2d}$ (d=2,3) backgrounds with Ramond-Ramond fluxes. Finally, applying the Buscher-like rules to T-dualising supergravity fields, we prove the T-self-duality of the whole class of the AdS$_d\times S^d \times M^{10-2d}$ superbackgrounds with Ramond-Ramond fluxes in the context of supergravity.
For three-dimensional ${\cal N}=4$ super Chern-Simons-matter theories associated to necklace quivers $U(N_0) \times U(N_1) \times \cdots U(N_{2r-1}) $, we study at quantum level the two kinds of 1/2 BPS Wilson loop operators recently introduced in arXiv:1506.07614. We perform a two-loop evaluation and find the same result for the two kinds of operators, so moving to higher loops a possible quantum uplift of the classical degeneracy. We also compute the 1/4 BPS bosonic Wilson loop and discuss the quantum version of the cohomological equivalence between fermionic and bosonic Wilson loops. We compare the perturbative result with the Matrix Model prediction and find perfect matching, after identification and remotion of a suitable framing factor. Finally, we discuss the potential appearance of three-loop contributions that might break the classical degeneracy and briefly analyse possible implications on the BPS nature of these operators.
We study a family of circular BPS Wilson loops in 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 N=4 SYM. We perform a complete two-loop analysis of their vacuum expectation value, discuss the framing dependence 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.
We evaluate ABJM observables at two loops, for any value of the rank N of the gauge group. We compute the color subleading contributions to the four-point scattering amplitude in ABJM at two loops. Contrary to the four dimensional case, IR divergent N-subleading contributions are proportional to leading poles in the regularization parameter. We then exploit the non-planar calculation for the amplitude to derive an expression for the two-loop Sudakov form factor at any N. In the planar limit the result coincides with the one recently obtained in literature by using Feynman diagrams and unitarity. Finally, we analyze the subleading contributions to the light-like four-cusps Wilson loop and interpret the result in terms of the non-abelian exponentiation theorem. All these perturbative results satisfy the uniform transcendentality principle, hinting at its validity in ABJM beyond the planar limit.