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We explicitly demonstrate the existence of static global defect solutions of arbitrary dimensionality whose energy does not diverge at spatial infinity, by considering maximally symmetric solutions described by an action with non-standard kinetic terms in a D+1 dimensional Minkowski space-time. We analytically determine the defect profile both at small and large distances from the defect centre. We verify the stability of such solutions and discuss possible implications of our findings, in particular for dark matter and charge fractionalization in graphene.
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The search for classically stable Type IIA de-Sitter vacua typically starts with an ansatz that gives Anti-de-Sitter supersymmetric vacua and then raises the cosmological constant by modifying the compactification. As one raises the cosmological constant, the couplings typically destabilize the classically stable vacuum, so the probability that this approach will lead to a classically stable de-Sitter vacuum is Gaussianly suppressed. This suggests that classically stable de-Sitter vacua in string theory (at least in the Type IIA region), especially those with relatively high cosmological constants, are very rare. The probability that a typical de-Sitter extremum is classically stable (i.e., tachyon-free) is argued to be Gaussianly suppressed as a function of the number of moduli.
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 initiate the study of intersecting surface operators/defects in four-dimensional quantum field theories (QFTs). We characterize these defects by coupled 4d/2d/0d theories constructed by coupling the degrees of freedom localized at a point and on intersecting surfaces in spacetime to each other and to the four-dimensional QFT. We construct supersymmetric intersecting surface defects preserving just two supercharges in N = 2 gauge theories. These defects are amenable to exact analysis by localization of the partition function of the underlying 4d/2d/0d QFT. We identify the 4d/2d/0d QFTs that describe intersecting surface operators in N = 2 gauge theories realized by intersecting M2-branes ending on N M5-branes wrapping a Riemann surface. We conjecture and provide evidence for an explicit equivalence between the squashed four-sphere partition function of these intersecting defects and correlation functions in Liouville/Toda CFT with the insertion of arbitrary degenerate vertex operators, which are labeled by representations of SU(N).
Based on an $e^{+}e^{-}$ collision data sample corresponding to an integrated luminosity of 2.93 $mathrm{fb}^{-1}$ collected with the BESIII detector at $sqrt{s}=3.773 mathrm{GeV}$, the first amplitude analysis of the singly Cabibbo-suppressed decay $D^{+}to K^+ K_S^0 pi^0$ is performed. From the amplitude analysis, the $K^*(892)^+ K_S^0$ component is found to be dominant with a fraction of $(57.1pm2.6pm4.2)%$, where the first uncertainty is statistical and the second systematic. In combination with the absolute branching fraction $mathcal{B}(D^+to K^+ K_S^0 pi^0)$ measured by BESIII, we obtain $mathcal{B}(D^+to K^*(892)^+ K_S^0)=(8.69pm0.40pm0.64pm0.51)times10^{-3}$, where the third uncertainty is due to the branching fraction $mathcal{B}(D^+to K^+ K_S^0 pi^0)$. The precision of this result is significantly improved compared to the previous measurement.
We consider quantum phase transitions with global symmetry breakings that result in the formation of topological defects. We evaluate the number densities of kinks, vortices, and monopoles that are produced in $d=1,2,3$ spatial dimensions respectively and find that they scale as $t^{-d/2}$ and evolve towards attractor solutions that are independent of the quench timescale. For $d=1$ our results apply in the region of parameters $lambda tau/m ll 1$ where $lambda$ is the quartic self-interaction of the order parameter, $tau$ is the quench timescale, and $m$ the mass parameter.
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