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Register a new userQuantum fluctuations of topological ${mathbb S}^3$-kinks
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The kink Casimir effect in the massive non-linear $S^3$-sigma model is analyzed.
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We study confining strings in ${cal{N}}=1$ supersymmetric $SU(N_c)$ Yang-Mills theory in the semiclassical regime on $mathbb{R}^{1,2} times mathbb{S}^1$. Static quarks are expected to be confined by double strings composed of two domain walls - which are lines in $mathbb{R}^2$ - rather than by a single flux tube. Each domain wall carries part of the quarks chromoelectric flux. We numerically study this mechanism and find that double-string confinement holds for strings of all $N$-alities, except for those between fundamental quarks. We show that, for $N_c ge 5$, the two domain walls confining unit $N$-ality quarks attract and form non-BPS bound states, collapsing to a single flux line. We determine the $N$-ality dependence of the string tensions for $2 le N_c le 10$. Compared to known scaling laws, we find a weaker, almost flat $N$-ality dependence, which is qualitatively explained by the properties of BPS domain walls. We also quantitatively study the behavior of confining strings upon increasing the $mathbb{S}^1$ size by including the effect of virtual $W$-bosons and show that the qualitative features of double-string confinement persist.
We consider string theory on AdS$_3$ $times$ (S$^3$ $times$ S$^3$ $times$ S$^1)/mathbb Z_2$, a background supporting $mathcal N=(3,3)$ spacetime supersymmetry. We propose that string theory on this background is dual to the symmetric product orbifold of $mathcal S_0/mathbb Z_2$ where $mathcal S_0$ is a theory of four free fermions and one free boson. We show that the BPS spectra of the two sides of the duality match precisely. Furthermore, we compute the elliptic genus of the dual CFT and that of the supergravity limit of string theory and demonstrate that they match, hence providing non-trivial support for the holographic proposal.
In these Lectures a method is described to analyze the effect of quantum fluctuations on topological defect backgrounds up to the one-loop level. The method is based on the spectral heat kernel/zeta function regularization procedure, and it is first applied to various types of kinks arising in several deformed linear and non-linear sigma models with different numbers of scalar fields. In the second part, the same conceptual framework is constructed for the topological solitons of the planar semilocal Abelian Higgs model, built from a doublet of complex scalar fields and one U(1) gauge field.
We compute free energies as well as conformal anomalies associated with boundaries for a conformal free scalar field. To that matter, we introduce the family of spaces of the form $mathbb{S}^atimes mathbb{H}^b$, which are conformally related to $mathbb{S}^{a+b}$. For the case of $a=1$, related to the entanglement entropy across $mathbb{S}^{b-1}$, we provide some new explicit computations of entanglement entropies at weak coupling. We then compute the free energy for spaces $mathbb{S}^atimes mathbb{H}^b$ for different values of $a$ and $b$. For spaces $mathbb{S}^{2n+1}times mathbb{H}^{2k}$ we find an exact match with the free energy on $mathbb{S}^{2n+2k+1}$. For $mathbb{H}^{2k+1}$ and $mathbb{S}^{3}times mathbb{H}^{3}$ we find conformal anomalies originating from boundary terms. We also compute the free energy for strongly coupled theories through holography, obtaining similar results.
Each hypersurface of a nearly Kahler manifold is naturally equipped with two tensor fields of $(1,1)$-type, namely the shape operator $A$ and the induced almost contact structure $phi$. In this paper, we show that, in the homogeneous NK $mathbb{S}^6$ a hypersurface satisfies the condition $Aphi+phi A=0$ if and only if it is totally geodesic; moreover, similar as for the non-flat complex space forms, the homogeneous nearly Kahler manifold $mathbb{S}^3timesmathbb{S}^3$ does not admit a hypersurface that satisfies the condition $Aphi+phi A=0$.
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