Exotic final states in the $$\varphi ^8$$ multi-kink collisions

We study final states in the scattering of kinks and antikinks of the $$\varphi ^8$$ φ 8 field-theoretic model. We use the initial conditions in the form of two, three or four static or moving kinks. In the numerical experiments we observe a number of different processes such as emergence of static and moving oscillons, change of the kink’s topological sector, scattering of an oscillon by a kink, production of kink–antikink pairs in oscillon–oscillon collisions. In antikink–kink collisions for asymmetric kinks, we found resonance phenomena – escape windows.

A comment on instantons and their fermion zero modes in adjoint QCD_2

The adjoint 2-dimensional QCD with the gauge group SU(N)/Z_NSU(N)/ZN admits topologically nontrivial gauge field configurations associated with nontrivial \pi_1[SU(N)/Z_N] = Z_Nπ1[SU(N)/ZN]=ZN. The topological sectors are labelled by an integer k=0,\ldots, N-1k=0,…,N−1. However, in contrast to QED_2QED2 and QCD_4QCD4, this topology is not associated with an integral invariant like the magnetic flux or Pontryagin index. These instantons may admit fermion zero modes, but there is always an equal number of left-handed and right-handed modes, so that the Atiyah-Singer theorem, which determines in other cases the number of the modes, does not apply. The mod. 2 argument [1] suggests that, for a generic gauge field configuration, there is either a single doublet of such zero modes or no modes whatsoever. However, the known solution of the Dirac problem for a wide class of gauge field configurations indicates the presence of k(N-k) zero mode doublets in the topological sector k. In this note, we demonstrate in an explicit way that these modes are not robust under a generic enough deformation of the gauge background and confirm thereby the conjecture of Ref. [1]. The implications for the physics of this theory (screening vs. confinement issue) are briefly discussed.

The topological line of ABJ(M) theory

We construct the one-dimensional topological sector of $$ \mathcal{N} $$ N = 6 ABJ(M) theory and study its relation with the mass-deformed partition function on S3. Supersymmetric localization provides an exact representation of this partition function as a matrix integral, which interpolates between weak and strong coupling regimes. It has been proposed that correlation functions of dimension-one topological operators should be computed through suitable derivatives with respect to the masses, but a precise proof is still lacking. We present non-trivial evidence for this relation by computing the two-point function at two-loop, successfully matching the matrix model expansion at weak coupling and finite ranks. As a by-product we obtain the two-loop explicit expression for the central charge cT of ABJ(M) theory. Three- and four-point functions up to one-loop confirm the relation as well. Our result points towards the possibility to localize the one-dimensional topological sector of ABJ(M) and may also be useful in the bootstrap program for 3d SCFTs.

Solitary oscillations and multiple antikink-kink pairs in the double sine-Gordon model

We study kink-antikink collisions in a particular case of the double sine-Gordon model depending on only one parameter r. The scattering process of large kink-antikink shows the changing of the topological sector. For some parameter intervals we observed two connected effects: the production of multiple antikink-kink pairs and up to three solitary oscillations. The scattering process for small kink-antikink has several possibilities: the changing of the topological sector, one-bounce collision, two-bounce collision, or formation of a bion state. In particular, we observed for small values of rand velocities, the formation of false two-bounce windows and the suppression of true two-bounce windows, despite the presence of an internal shape mode.

The grin of Cheshire cat resurgence from supersymmetric localization

First we compute the \mbox{S}^2S2 partition function of the supersymmetric \mathbb{CP}^{N-1}ℂℙN−1 model via localization and as a check we show that the chiral ring structure can be correctly reproduced. For the \mathbb{CP}^1ℂℙ1 case we provide a concrete realisation of this ring in terms of Bessel functions. We consider a weak coupling expansion in each topological sector and write it as a finite number of perturbative corrections plus an infinite series of instanton-anti-instanton contributions. To be able to apply resurgent analysis we then consider a non-supersymmetric deformation of the localized model by introducing a small unbalance between the number of bosons and fermions. The perturbative expansion of the deformed model becomes asymptotic and we analyse it within the framework of resurgence theory. Although the perturbative series truncates when we send the deformation parameter to zero we can still reconstruct non-perturbative physics out of the perturbative data in a nice example of Cheshire cat resurgence in quantum field theory. We also show that the same type of resurgence takes place when we consider an analytic continuation in the number of chiral fields from NN to r\in\mathbb{R}r∈ℝ. Although for generic real rr supersymmetry is still formally preserved, we find that the perturbative expansion of the supersymmetric partition function becomes asymptotic so that we can use resurgent analysis and only at the end take the limit of integer rr to recover the undeformed model.

Topological Susceptibility under Gradient Flow

We study the impact of the Gradient Flow on the topology in various models of lattice field theory. The topological susceptibility Xt is measured directly, and by the slab method, which is based on the topological content of sub-volumes (“slabs”) and estimates Xt even when the system remains trapped in a fixed topological sector. The results obtained by both methods are essentially consistent, but the impact of the Gradient Flow on the characteristic quantity of the slab method seems to be different in 2-flavour QCD and in the 2d O(3) model. In the latter model, we further address the question whether or not the Gradient Flow leads to a finite continuum limit of the topological susceptibility (rescaled by the correlation length squared, ξ2). This ongoing study is based on direct measurements of Xt in L × L lattices, at L/ξ ≃6.