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The N = 8 Superconformal Bootstrap in Three Dimensions
, 2014
"... We analyze the constraints imposed by unitarity and crossing symmetry on the fourpoint function of the stresstensor multiplet of N = 8 superconformal field theories in three dimensions. We first derive the superconformal blocks by analyzing the superconformal Ward identity. Our results imply that ..."
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We analyze the constraints imposed by unitarity and crossing symmetry on the fourpoint function of the stresstensor multiplet of N = 8 superconformal field theories in three dimensions. We first derive the superconformal blocks by analyzing the superconformal Ward identity. Our results imply that the OPE of the primary operator of the stresstensor multiplet with itself must have parity symmetry. We then analyze the relations between the crossing equations, and we find that these equations are mostly redundant. We implement the independent crossing constraints numerically and find bounds on OPE coefficients and operator dimensions as a function of the stresstensor central charge. To make contact with known N = 8 superconformal field theories, we compute this central charge in a few particular cases using supersymmetric localization. For limiting values of the central charge, our numerical bounds are nearly saturated by the large N limit of ABJM theory and also by the free U(1) × U(1) ABJM theory.
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, 2006
"... Abstract: We consider pure spinor strings that propagate in the background generated by a sequence of TsT transformations. We use the fact that U(1) isometry variables of TsTtransformed background are related to the isometry variables of the initial background in the universal way that is independe ..."
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Abstract: We consider pure spinor strings that propagate in the background generated by a sequence of TsT transformations. We use the fact that U(1) isometry variables of TsTtransformed background are related to the isometry variables of the initial background in the universal way that is independent of the details of the background. We will argue that after redefinitions of pure spinors and the fermionic variables we can construct pure spinor action with manifest U(1) isometry. This fact implies that the pure spinor string in TsTtransformed background is described by pure spinor string in the original background where worldvolume modes are subject to twisted boundary conditions. We will argue that these twisted boundary conditions generally prevent to prove the quantum conformal invariance of the pure spinor string in AdS5 × S 5 background. We determine the conditions under which this quantum conformal invariance can be proved. We also determine the Lax pair for pure spinor strings in the TsTtransformed background.
Preprint typeset in JHEP style PAPER VERSION The spectral problem of the ABJ Fermi gas
"... Abstract: The partition function on the threesphere of ABJ theory can be rewritten into a partition function of a noninteracting Fermi gas, with an accompanying oneparticle Hamiltonian. We study the spectral problem defined by this Hamiltonian. We determine the exact WKB quantization condition, ..."
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Abstract: The partition function on the threesphere of ABJ theory can be rewritten into a partition function of a noninteracting Fermi gas, with an accompanying oneparticle Hamiltonian. We study the spectral problem defined by this Hamiltonian. We determine the exact WKB quantization condition, which involves quantities from refined topological string theory, and test it successfully against numerical calculations of the spectrum. ar X iv
ON THE GROWTH OF SUDLER’S SINE PRODUCT ∏n r=1 2 sinpirω AT THE GOLDEN ROTATION NUMBER
"... Abstract. We study the growth at the golden rotation number ω = ( 5 − 1)/2 of the function sequence Pn(ω) = ∏n r=1 2 sinpirω. This sequence has been variously studied elsewhere as a skew product of sines, Birkhoff sum, qPochhammer symbol (on the unit circle), and restricted Euler function. In par ..."
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Abstract. We study the growth at the golden rotation number ω = ( 5 − 1)/2 of the function sequence Pn(ω) = ∏n r=1 2 sinpirω. This sequence has been variously studied elsewhere as a skew product of sines, Birkhoff sum, qPochhammer symbol (on the unit circle), and restricted Euler function. In particular we study the Fibonacci decimation of the sequence Pn, namely the subsequence Qn = ∣∣∣∏Fnr=1 2 sinpirω∣∣ ∣ for Fibonacci numbers Fn, and prove that this renormalisation subsequence converges to a constant. From this we show rigorously that the growth of Pn(ω) is bounded by power laws. This provides the theoretical basis to explain recent experimental results reported by Knill and Tangerman (Selfsimilarity and growth in Birkhoff sums for the golden rotation. Nonlinearity, 24(11):3115–3127, 2011).