Numerical results for the exact spectrum of planar AdS4/CFT3

We compute the anomalous dimension for a short single-trace operator in planar ABJM theory at intermediate coupling. This is done by solving numerically the set of Thermodynamic Bethe Ansatz equations which are expected to describe the exact spectrum of the theory. We implement a truncation method which significantly reduces the number of integral equations to be solved and improves numerical efficiency. Results are obtained for a range of 't Hooft coupling lambda corresponding to $0 \leq h(\lambda) \leq 1$, where h(lambda) is the interpolating function of the AdS4/CFT3 Bethe equations.Comment: v3: corrected Acknowledgements section; v4: minor changes, published version; v5: fixed typos in Eq. (3.9

Analytic Solution of Bremsstrahlung TBA

We consider the quark--anti-quark potential on the three sphere or the generalized cusp anomalous dimension in planar N=4 SYM. We concentrate on the vacuum potential in the near BPS limit with $L$ units of R-charge. Equivalently, we study the anomalous dimension of a super-Wilson loop with L local fields inserted at a cusp. The system is described by a recently proposed infinite set of non-linear integral equations of the Thermodynamic Bethe Ansatz (TBA) type. That system of TBA equations is very similar to the one of the spectral problem but simplifies a bit in the near BPS limit. Using techniques based on the Y-system of functional equations we first reduced the infinite system of TBA equations to a Finite set of Nonlinear Integral Equations (FiNLIE). Then we solve the FiNLIE system analytically, obtaining a simple analytic result for the potential! Surprisingly, we find that the system has equivalent descriptions in terms of an effective Baxter equation and in terms of a matrix model. At L=0, our result matches the one obtained before using localization techniques. At all other L's, the result is new. Having a new parameter, L, allows us to take the large L classical limit. We use the matrix model description to solve the classical limit and match the result with a string theory computation. Moreover, we find that the classical string algebraic curve matches the algebraic curve arising from the matrix model.Comment: 50 pages, 5 figures. v2: references added, JHEP versio

On contractions of classical basic superalgebras

We define a class of orthosymplectic $osp(m;j|2n;\omega)$ and unitary $sl(m;j|n;\epsilon)$ superalgebras which may be obtained from $osp(m|2n)$ and $sl(m|n)$ by contractions and analytic continuations in a similar way as the special linear, orthogonal and the symplectic Cayley-Klein algebras are obtained from the corresponding classical ones. Casimir operators of Cayley-Klein superalgebras are obtained from the corresponding operators of the basic superalgebras. Contractions of $sl(2|1)$ and $osp(3|2)$ are regarded as an examples.Comment: 15 pages, Late

Quark--anti-quark potential in N=4 SYM

We construct a closed system of equations describing the quark--anti-quark potential at any coupling in planar N=4 supersymmetric Yang-Mills theory. It is based on the Quantum Spectral Curve method supplemented with a novel type of asymptotics. We present a high precision numerical solution reproducing the classical and one-loop string predictions very accurately. We also analytically compute the first 7 nontrivial orders of the weak coupling expansion. Moreover, we study analytically the generalized quark--anti-quark potential in the limit of large imaginary twist to all orders in perturbation theory. We demonstrate how the QSC reduces in this case to a one-dimensional Schrodinger equation. In the process we establish a link between the Q-functions and the solution of the Bethe-Salpeter equation.Comment: 31 pages, 1 figure; v2: minor correcton

Quantum Spectral Curve at Work: From Small Spin to Strong Coupling in N=4 SYM

We apply the recently proposed quantum spectral curve technique to the study of twist operators in planar N=4 SYM theory. We focus on the small spin expansion of anomalous dimensions in the sl(2) sector and compute its first two orders exactly for any value of the 't Hooft coupling. At leading order in the spin S we reproduced Basso's slope function. The next term of order S^2 structurally resembles the Beisert-Eden-Staudacher dressing phase and takes into account wrapping contributions. This expansion contains rich information about the spectrum of local operators at strong coupling. In particular, we found a new coefficient in the strong coupling expansion of the Konishi operator dimension and confirmed several previously known terms. We also obtained several new orders of the strong coupling expansion of the BFKL pomeron intercept. As a by-product we formulated a prescription for the correct analytical continuation in S which opens a way for deriving the BFKL regime of twist two anomalous dimensions from AdS/CFT integrability.Comment: 53 pages, references added; v3: due to a typo in the coefficients C_2 and D_2 on page 29 we corrected the rational part of the strong coupling predictions in equations (1.5-6), (6.22-24), (6.27-30) and in Table

QCD properties of twist operators in the N=6 Chern-Simons theory

We consider twist-1, 2 operators in planar N=6 superconformal Chern-Simons ABJM theory. We derive higher order anomalous dimensions from integrability and test various QCD-inspired predictions known to hold in N=4 SYM. In particular, we show that the asymptotic anomalous dimensions display intriguing remnants of Gribov-Lipatov reciprocity and Low-Burnett-Kroll logarithmic cancellations. Wrapping effects are also discussed and shown to be subleading at large spin.Comment: 22 pages, expanded reference

Wrapping corrections, reciprocity and BFKL beyond the sl(2) subsector in N=4 SYM

We consider N=4 SYM and a class of spin N, length-3, twist operators beyond the well studied sl(2) subsector. They can be identified at one-loop with three gluon operators. At strong coupling, they are associated with spinning strings with two spins in AdS5. We exploit the Y-system to compute the leading weak-coupling four loop wrapping correction to their anomalous dimension. The result is written in closed form as a function of the spin N. We combine the wrapping correction with the known four-loop asymptotic Bethe Ansatz contribution and analyze special limits in the spin N. In particular, at large N, we prove that a generalized Gribov-Lipatov reciprocity holds. At negative unphysical spin, we present a simple BFKL-like equation predicting the rightmost leading poles.Comment: 18 page

Searching for Hyperbolicity

This is an expository paper, based on by a talk given at the AWM Research Symposium 2017. It is intended as a gentle introduction to geometric group theory with a focus on the notion of hyperbolicity, a theme that has inspired the field from its inception to current-day research

Fermionic determinant for dyons and instantons with nontrivial holonomy

We calculate exactly the functional determinant for fermions in fundamental representation of SU(2) in the background of periodic instanton with non-trivial value of the Polyakov line at spatial infinity. The determinant depends on the value of the holonomy v, the temperature, and the parameter r_12, which at large values can be treated as separation between the Bogomolny--Prasad--Sommerfeld monopoles (or dyons) which constitute the periodic instanton. We find a compact expression for small and large r_12 and compute the determinant numerically for arbitrary r_12 and v.Comment: 17 pages, published version, references adde

On three-manifolds dominated by circle bundles

We determine which three-manifolds are dominated by products. The result is that a closed, oriented, connected three-manifold is dominated by a product if and only if it is finitely covered either by a product or by a connected sum of copies of the product of the two-sphere and the circle. This characterization can also be formulated in terms of Thurston geometries, or in terms of purely algebraic properties of the fundamental group. We also determine which three-manifolds are dominated by non-trivial circle bundles, and which three-manifold groups are presentable by products.Comment: 12 pages; to appear in Math. Zeitschrift; ISSN 1103-467