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The torus is special because it's so simple, and because it provides the most tractable example of Mirror Symmetry https://en.wikipedia.org/wiki/Mirror_symmetry_(string_theory), a generalization of T-duality (which relates Type IIB with Type IIA with one another). Toric compactifications are rather special, they're a special case of an incredibly large ...


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This is the half-joke explanation I give to undergrads who work on LHC SUSY searches: Start with SM diagrams Replace quark with corresponding squark Replace $W^\pm$ with $\tilde{\chi}^\pm$ Impose the conservation of twiddles (R-parity) The neutrilino ($\tilde{\chi}^0$) caries one unit twiddle and couples to anything a $W$, $Z$, or $H$ would couple to. ...


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As you can find on google, or in any book of supersymmetry, the number of components of a spinor in dimension $d$ is $2^{[d/2]}$. Where $[d/2]$ denotes the integer part of $d/2$. In certain dimensions you can impose a further property: the Majorana condition on your spinor, that reduces further of a factor of $2$ the number of independent (real) components. ...


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As a beginner for working on relevant topics, I just write few words about your question. I hope it helps you up. Localization Principle has been great role in computing superconformal index also it gives the exact calculation in susy gauge theories. From some excellent works by Pestun, Kapustin, Willet and so on(about a decade ago?), many researcher now ...


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In fact the answer is "yes", the non-chiral type $II$ sugra thoery is called type $II$ A. You can obtain it by dimensional reduction from the $M$-theory sugra in $d=11$. The (massless) spectrum of type $II$ B contains spinor representations of just one chirality (which one is matter of convention), while type $II$ A contains representations of both ...


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Because you want the maximal spin particle allowed to be 2 (since there is no higher spin field theory interacting non trivially), thus in a supermultiplet starting with a particle with helicity $0$, say in $d=4$, the maximal number of susy you can apply is $8$, thus $N=8$ in $d=4$ is the maximal supersymmetry admitted, which means $32$ supercharges.


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In the representation theory of Virasoro algebra there is a mathematically strict theorem: http://en.wikipedia.org/wiki/Goddard%E2%80%93Thorn_theorem for bosonic string theory, and similarly for superstring theory. Intuitively the critical dimensions come from zeta function regularization.


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In the textbook of TASI 2009, section "Introduction to extra dimension" i can find the answer as follows. They state that $5D$ or higher dimensional gauge coupling has a negative mass dimension, so the 5d or higher dimensional gauge theory is non-renormalizable.


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A more colloquial way of understanding this is to write down the expressions for loop corrections in a SUSY gauge theory. The important ingredient is that in addition to the gauge bosons you will also have gauginos, i.e. fermions in the adjoint representation. To understand how a vacuum diagram vanishes thing about how a gauge boson in 4D has two ...



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