We study the multi-boundary entanglement structure of the state associated with the torus link complement $S^3 \backslash T_{p,q}$ in the set-up of three-dimensional SU(2)$_k$ Chern-Simons theory. The focal point of this work is the asymptotic behavior of the Rényi entropies, including the entanglement entropy, in the semiclassical limit of $k \to \infty$. We present a detailed analysis for several torus links and observe that the entropies converge to a finite value in the semiclassical limit. We further propose that the large $k$ limiting value of the Rényi entropy of torus links of type $T_{p,pn}$ is the sum of two parts: (i) the universal part which is independent of $n$, and (ii) the non-universal or the linking part which explicitly depends on the linking number $n$. Using the analytic techniques, we show that the universal part comprises of Riemann zeta functions and can be written in terms of the partition functions of two-dimensional topological Yang-Mills theory. More precisely, it is equal to the Rényi entropy of certain states prepared in topological $2d$ Yang-Mills theory with SU(2) gauge group. Further, the universal parts appearing in the large $k$ limits of the entanglement entropy and the minimum Rényi entropy for torus links $T_{p,pn}$ can be interpreted in terms of the volume of the moduli space of flat connections on certain Riemann surfaces. We also analyze the Rényi entropies of $T_{p,pn}$ link in the double scaling limit of $k \to \infty$ and $n \to \infty$ and propose that the entropies converge in the double limit as well.
We investigate the presence of vortex configurations in generalized Maxwell-Chern-Simons models with nonminimal coupling, in which we introduce a function that modifies the dynamical term of the scalar field in the Lagrangian. We first follow a route already considered in previous works to develop the Bogomol'nyi procedure, and, in this context, we use the first order equations to obtain a vortex with a novel behavior at its core. We then go further and introduce a novel procedure to develop the Bogomol'nyi methodology. It supports distinct first order equations, and we then investigate anothe…
We have shown the existence of self-dual solitons in a type of generalized Chern-Simons baby Skyrme model where the generalized function (depending only in the Skyrme field) is coupled to the sigma-model term. The consistent implementation of the Bogomol'nyi-Prasad-Sommerfield (BPS) formalism requires the generalizing function becomes the superpotential defining properly the self-dual potential. Thus, we have obtained a topological energy lower-bound (Bogomol'nyi bound) and the self-dual equations satisfied by the fields saturating such a bound. The Bogomol'nyi bound being proportional to the …
We verify the existence of radially symmetric first-order solitons in a gauged $CP(2)$ scenario in which the dynamics of the Abelian gauge field is controlled by the Maxwell-Chern-Simons action. We implement the standard Bogomol'nyi-Prasad-Sommerfield (BPS) formalism, from which we obtain a well-defined lower bound for the corresponding energy (i.e. the Bogomol'nyi bound) and the first-order equations saturating it. We solve these first-order equations numerically by means of the finite-difference scheme, therefore obtaining regular solutions of the effective model, their energy being quantize…
In this work, we propose an exponentially generalized Abelian model. We investigated the presence of vortex structures in models coupled to Maxwell and Chern-Simons fields. We chose to investigate the dynamics of the complex scalar field in models coupled separately to the Maxwell term and the Chern-Simons term. For this, we analyze the Bogomol'nyi equations in both cases to describe the static field configurations. An interesting result appears when we note that scalar field solutions generate degenerate minimum energy configurations by a factor of $ν^{2}$ in Maxwell's case. On the other hand…
In this work, we investigated the existence of compacton-like configuration in the O(3)-sigma model. We consider a minimally coupled O(3)-sigma model with a gauge field governed by a generalized Chern-Simons term. Contrary to that established in the literature, we impose a new set of boundary conditions and, we find solutions of the variable fields and the respective energy density in the Bogomol'nyi limit. On the other hand, the introduction of a parameter $ω$ in the Chern-Simons term can be adjusted to leads to finite-energy solutions of the model. Moreover, compact-like structures were stud…
We present a self-dual parity-invariant $U(1) \times U(1)$ Maxwell-Chern-Simons scalar $\text{QED}_3$. We show that the energy functional admits a Bogomol'nyi-type lower bound, whose saturation gives rise to first order self-duality equations. We perform a detailed analysis of this system, discussing its main features and exhibiting explicit numerical solutions corresponding to finite-energy topological vortices and non-topological solitons. The mixed Chern-Simons term plays an important role here, ensuring the main properties of the model and suggesting possible applications in condensed matt…
The semiclassical approximation for the Chern-Simons partition function
本文用不变积分方法导出了陈-西蒙斯规范理论中配分函数的半经典近似。在此框架中自动考虑了以前推导中未确定和必须手工确定的体积和比例系数。对于规范群SU（2）和时空S^3，S^2 x S^1，S^1 x S^1 x S^1和L（p，q），证明了在弱耦合（大k）极限下配分函数与Witten精确表达式的一致性.
We show that generic three-dimensional $\mathcal N=2$ quiver super Chern-Simons-matter theories admit Bogomol'nyi-Prasad-Sommerfield (BPS) Drukker-Trancanelli (DT) type Wilson loops. We investigate both Wilson loops along timelike infinite straight lines in Minkowski spacetime and circular Wilson loops in Euclidean space. In Aharnoy-Bergman-Jafferis-Maldacena theory, we find that generic BPS DT type Wilson loops preserve the same number of supersymmetries as Gaiotto-Yin type Wilson loops. There are several free parameters for generic BPS DT type Wilson loops in the construction, and supersymme…
We consider a gauged $CP(2)$ theory in the presence of the Chern-Simons action, focusing our attention on those time-independent solutions possessing radial symmetry. In this context, we develop a coherent first-order framework via the Bogomol'nyi prescription, from which we obtain the corresponding energy lower-bound and the first-order equations the model supports. We use these expressions to introduce effective BPS scenarios, solving the resulting first-order equations by means of the finite-difference scheme, this way attaining genuine field solutions engendering topological configurations…
Notes on Yang-Mills--Higgs monopoles and dyons on R^D, and Chern-Simons--Higgs solitons on \R^{D-2}: Dimensional reduction of Chern-Pontryagin densities
We investigate the existence of first-order vortices inherent to both the Maxwell-Chern-Simons-Higgs and the Maxwell-Chern-Simons-$CP(2)$ models extended via the inclusion of an extra scalar sector which plays the role of a source field. For both cases, we focus our attention on the time-independent configurations with radial symmetry which can be obtained through the implementation of the so-called Bogomol'nyi-Prasad-Sommerfield (BPS) prescription. In this sense, in order to solve the corresponding first-order differential equations, we introduce some particular scenarios which are driven by …
We consider SU(N) Chern-Simons theory coupled to a scalar field in the fundamental representation at strictly zero temperature and finite chemical potential for the global U(1)_B particle number or flavour symmetry. In the semiclassical regime we identify a Bose condensed ground state with a vacuum expectation value (VEV) for the scalar accompanied by noncommuting background gauge field matrix VEVs. These matrices coincide with the droplet ground state of the Abelian quantum Hall matrix model. The ground state spontaneously breaks U(1)_B and Higgses the gauge group whilst preserving spatial ro…
We find that an S-duality in SL(2) Chern-Simons theory for hyperbolic 3-manifolds emerges by the Borel resummation of a semiclassical expansion around a particular flat connection associated to the hyperbolic structure. We demonstrate it numerically with two representative examples of hyperbolic 3-manifolds.
We have studied the existence de self-dual solitons in a gauged version of the baby Skyrme model in which the gauge field dynamics is governed by the Maxwell-Chern-Simons action. For such a purpose, we have developed a detailed implementation of the Bogomol'nyi-Prasad-Sommerfield formalism providing the self-dual equations whose solutions saturate the energy lower bound. Such a bound related to the topological charge of the Skyrme field becomes quantized whereas both the total magnetic flux and the total electrical charge are not. We have found two types of self-dual Skyrme field profiles: the…
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 param…
We present an improved formulation of 4-dimensional Lorentzian spinfoam quantum gravity with cosmological constant. The construction of spinfoam amplitudes uses the state-integral model of PSL(2,$\mathbb{C}$) Chern-Simons theory and the implementation of simplicity constraint. The formulation has 2 key features: (1) spinfoam amplitudes are all finite, and (2) With suitable boundary data, the semiclassical asymptotics of the vertex amplitude has two oscillatory terms, with phase plus or minus the 4-dimensional Lorentzian Regge action with cosmological constant for the constant curvature 4-simpl…
The simplicity constraint is studied in the context of 4d spinfoam models with cosmological constant. We find that the quantum simplicity constraint is realized as the 2d surface defect in SL(2,$\mathbb{C}$) Chern-Simons theory in the construction of spinfoam amplitudes. By this realization of simplicity constraint in Chern-Simons theory, we are able to construct the new spinfoam amplitude with cosmological constant for arbitrary simplicial complex (with many 4-simplices). The semiclassical asymptotics of the amplitude is shown to reproduce correctly the 4-dimensional Einstein-Regge action wit…
We solve for finite $N$ the matrix model of supersymmetric $U(N)$ Chern-Simons theory coupled to $N_{f}$ fundamental and $N_{f}$ anti-fundamental chiral multiplets of $R$-charge $1/2$ and of mass $m$, by identifying it with an average of inverse characteristic polynomials in a Stieltjes-Wigert ensemble. This requires the computation of the Cauchy transform of the Stieltjes-Wigert polynomials, which we carry out, finding a relationship with Mordell integrals, and hence with previous analytical results on the matrix model. The semiclassical limit of the model is expressed, for arbitrary $N_{f},$…
A correspondence between three-dimensional flat connections and constant curvature four-dimensional simplices is used to give a novel quantization of geometry via complex SL(2,C) Chern-Simons theory. The resulting quantum geometrical states are hence represented by the 3d blocks of analytically continued Chern-Simons theory. In the semiclassical limit of this quantization the three-dimensional Chern-Simons action, remarkably, becomes the discrete Einstein-Hilbert action of a 4-simplex, featuring the appropriate boundary terms as well as the essential cosmological term proportional to the simpl…
We compute partition functions of Chern-Simons type theories for cylindrical spacetimes $I \times Σ$, with $I$ an interval and $\dim Σ= 4l+2$, in the BV-BFV formalism (a refinement of the Batalin-Vilkovisky formalism adapted to manifolds with boundary and cutting-gluing). The case $\dim Σ= 0$ is considered as a toy example. We show that one can identify - for certain choices of residual fields - the "physical part" (restriction to degree zero fields) of the BV-BFV effective action with the Hamilton-Jacobi action computed in the companion paper [arXiv:2012.13270], without any quantum correction…
