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I think I can answer my question now. The Lieb's theorem here is a statement about which flux configuration (or flux configurations) minimizes the ground state energy of the quadratic Hamiltonians with each corresponding flux configuration/sector. In the case that $J_x=J_y=0$ (or more generic cases that $J_xJ_yJ_z=0$), the corresponding $x,y$ link terms are ...


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The answer is yes; this can be shown by evaluating the variation of the action. The action consists of three terms, we will consider them separately: $$\delta_\epsilon K(\Phi,\bar{\Phi})=\frac{\partial K(\Phi,\bar{\Phi})}{\partial\Phi^i}\delta_\epsilon \Phi^i+\frac{\partial K(\Phi,\bar{\Phi})}{\partial\bar{\Phi}_i}\delta_\epsilon\bar{\Phi}_i=i\epsilon K_i ...


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First of all there is no proof of this statement. It is just a general expectation that the more symmetries you have the more reason to expect better quantum properties. This works with SUSY, the more SUSY you have the better the theory is at the quantum level, say $N=4$ SYM, or $N=8$ SUGRA that some people still have hope to be well-defined. If you involve ...


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I think K-K is still of much research interest. The K-K theory, which unifies YM fields and gravity are there since a long time. However, these theories have some consistency problems. In the original K-K theory, it was assumed that the 5D metric functions do not depend on the 5-th coordinate. This was the main reason of inconsistency. If the 5th ...


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First let me refer you to Eric Weinberg's book where the instanton moduli space is described in more detail. Principal bundles over 4-dimensional Riemannian manifolds are classified by the second Chern class = Instanton number and the t' Hooft discrete Abelian magnetic fluxes. Please see the following Lecture notes by Måns Henningson. t' Hooft fluxes ...


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There is an explicitly three-dimensional version of a Hawking-Page transition in AdS space. It is given by a transition between an asymptotically $AdS_3$ spacetime and the BTZ (Bañados-Teitelboim-Zanelli) black hole. The line element of thermal (euclidean) $AdS_3$ space is given by ...



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