The dynamics of both global and local vortices with non-Abelian orientational moduli is investigated in detail. Head-on collisions of these vortices are numerically simulated for parallel, anti-parallel and orthogonal internal orientations where we f
ind interesting dynamics of the orientational moduli. A detailed study of the inter-vortex force is provided and a phase diagram separating Abelian and non-Abelian vortex types is constructed. Some results on scatterings with non-zero impact parameter and multi-vortex collisions are included.
We study holographic subregion volume complexity for a line segment in the AdS$_3$ Vaidya geometry. On the field theory side, this gravity background corresponds to a sudden quench which leads to the thermalization of the strongly-coupled dual confor
mal field theory. We find the time-dependent extremal volume surface by numerically solving a partial differential equation with boundary condition given by the Hubeny-Rangamani-Takayanagi surface, and we use this solution to compute holographic subregion complexity as a function of time. Approximate analytical expressions valid at early and at late times are derived.
We explore in detail the properties of two melonic quantum mechanical theories which can be formulated either as fermionic matrix quantum mechanics in the new large $D$ limit, or as disordered models. Both models have a mass parameter $m$ and the tra
nsition from the perturbative large $m$ region to the strongly coupled black-hole small $m$ region is associated with several interesting phenomena. One model, with ${rm U}(n)^2$ symmetry and equivalent to complex SYK, has a line of first-order phase transitions terminating, for a strictly positive temperature, at a critical point having non-trivial, non-mean-field critical exponents for standard thermodynamical quantities. Quasi-normal frequencies, as well as Lyapunov exponents associated with out-of-time-ordered four-point functions, are also singular at the critical point, leading to interesting new critical exponents. The other model, with reduced ${rm U}(n)$ symmetry, has a quantum critical point at strictly zero temperature and positive critical mass $m_*$. For $0<m<m_*$, it flows to a new gapless IR fixed point, for which the standard scale invariance is spontaneously broken by the appearance of distinct scaling dimensions $Delta_+$ and $Delta_-$ for the Euclidean two-point function when $trightarrow +infty$ and $trightarrow -infty$ respectively. We provide several detailed and pedagogical derivations, including rigorous proofs or simplified arguments for some results that were already known in the literature.
A recent proposal was made for a large representation rank limit for which the expectation values of N = 4 super Yang-Mills Wilson loops are given by the exponential of the 1-loop result. We verify the validity of this exponentiation in the strong co
upling limit using the holographic D3-brane description for straight Wilson loops following an arbitrary internal space trajectory.
We study the cusped Wilson line operators and Bremsstrahlung functions associated to particles transforming in the rank-$k$ symmetric representation of the gauge group $U(N)$ for ${cal N} = 4$ super Yang-Mills. We find the holographic D3-brane descri
ption for Wilson loops with internal cusps in two different limits: small cusp angle and $ksqrt{lambda}gg N$. This allows for a non-trivial check of a conjectured relation between the Bremsstrahlung function and the expectation value of the 1/2 BPS circular loop in the case of a representation other than the fundamental. Moreover, we observe that in the limit of $kgg N$, the cusped Wilson line expectation value is simply given by the exponential of the 1-loop diagram. Using group theory arguments, this eikonal exponentiation is conjectured to take place for all Wilson loop operators in symmetric representations with large $k$, independently of the contour on which they are supported.
We compute the strong coupling limit of the boundary reflection factor for excitations on open strings attached to various kinds of D5-branes that probe AdS5 x S5. We study the crossing equation, which constrains the boundary reflection factor, and p
ropose that some solutions will give the boundary reflection factors for all values of the coupling. Our proposal passes various checks in the strong coupling limit by comparison with diverse explicit string theory computations. In some of the cases we consider, the D5-branes correspond to 1/2 BPS Wilson loops in the k-th rank antisymmetric representation of the dual field theory. In the other cases they correspond in the dual field theory to the addition of a fundamental hypermultiplet in a defect.
