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Arkady A Tseytlin - One of the best experts on this subject based on the ideXlab platform.
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Partition Function of free conformal higher spin theory
Journal of High Energy Physics, 2014Co-Authors: Matteo Beccaria, Xavier Bekaert, Arkady A TseytlinAbstract:We compute the canonical Partition Function Z of non-interacting conformal higher spin (CHS) theory viewed as a collection of free spin s CFT's in R d . We discuss in detail the 4-dimensional case (where s = 1 is the standard Maxwell vector, s = 2 is the Weyl graviton, etc.), but also present a generalization for all even dimensions d. Z may be found by counting the numbers of conformal operators and their descendants (modulo gauge identities and equations of motion) weighted by scaling dimensions. This conformal operator counting method requires a careful analysis of the structure of characters of rele- vant (conserved current, shadow field and conformal Killing tensor) representations of the conformal algebra so(d,2). There is also a close relation to massless higher spin Partition Functions with alternative boundary conditions in AdSd+1. The same Partition Function Z may also be computed from the CHS path integral on a curved S 1 × S d−1 background. This allows us to determine a simple factorized form of the CHS kinetic operator on this conformally flat background. Summing the individual conformal spin contributions Zs over all spins we obtain the total Partition Function of the CHS theory. We also find the corresponding Casimir energy on the sphere and show that it vanishes if one uses the same regularization prescription that implies the cancellation of the total conformal anomaly a-coefficient. This happens to be true in all even dimensionsd ≥ 2.
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on Partition Function and weyl anomaly of conformal higher spin fields
Nuclear Physics, 2013Co-Authors: Arkady A TseytlinAbstract:Abstract We study 4-dimensional higher-derivative conformal higher-spin (CHS) fields generalizing Weyl graviton and conformal gravitino. They appear, in particular, as “induced” theories in the AdS/CFT context. We consider their Partition Function on curved Einstein-space backgrounds like (A)dS or sphere and Ricci-flat spaces. Remarkably, the bosonic (integer spin s ) CHS Partition Function appears to be given by a product of Partition Functions of the standard 2nd-derivative “partially massless” spin s fields, generalizing the previously known expression for the 1-loop Weyl graviton ( s = 2 ) Partition Function. We compute the corresponding spin s Weyl anomaly coefficients a s and c s . Our result for a s reproduces the expression found recently in arXiv:1306.5242 by an indirect method implied by AdS/CFT (which relates the Partition Function of a CHS field on S 4 to a ratio of known Partition Functions of massless higher-spin field in AdS 5 with alternate boundary conditions). We also obtain similar results for the fermionic CHS fields. In the half-integer s case the CHS Partition Function on (A)dS background is given by the product of squares of “partially massless” spin s Partition Functions and one extra factor corresponding to a special massive conformally invariant spin s field. It was noticed in arXiv:1306.5242 that the sum of the bosonic a s coefficients over all s is zero when computed using the ζ -Function regularization, and we observe that the same property is true also in the fermionic case.
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green schwarz string in ads5 s5 semiclassical Partition Function
Journal of High Energy Physics, 2000Co-Authors: David J Gross, Nadav Drukker, Arkady A TseytlinAbstract:A systematic approach to the study of semiclassical fluctuations of strings in AdS5 ? S5 based on the Green-Schwarz formalism is developed. We show that the string Partition Function is well defined and finite. Issues related to different gauge choices are clarified. We consider explicitly several cases of classical string solutions with the world surface ending on a line, on a circle or on two lines on the boundary of AdS. The first example is a BPS object and the Partition Function is one. In the third example the determinants we derive should give the first corrections to the Wilson loop expectation value in the strong coupling expansion of the = 4 SYM theory at large N.
Matteo Beccaria - One of the best experts on this subject based on the ideXlab platform.
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Partition Function of free conformal higher spin theory
Journal of High Energy Physics, 2014Co-Authors: Xavier Bekaert, Tseytlin Arkady, Matteo BeccariaAbstract:We compute the canonical Partition Function Z of non-interacting conformal higher spin (CHS) theory viewed as a collection of free spin s CFT's in R^d. We discuss in detail the 4-dimensional case (where s=1 is the standard Maxwell vector, s=2 is the Weyl graviton, etc.), but also present a generalization for all even dimensions d. Z may be found by counting the numbers of conformal operators and their descendants (modulo gauge identities and equations of motion) weighted by scaling dimensions. This conformal operator counting method requires a careful analysis of the structure of characters of relevant (conserved current, shadow field and conformal Killing tensor) representations of the conformal algebra so(d,2). There is also a close relation to massless higher spin Partition Functions with alternative boundary conditions in AdS_{d+1}. The same Partition Function Z may also be computed from the CHS path integral on a curved S^1 x S^{d-1} background. This allows us to determine a simple factorized form of the CHS kinetic operator on this conformally flat background. Summing the individual conformal spin contributions Z_s over all spins we obtain the total Partition Function of the CHS theory. We also find the corresponding Casimir energy and show that it vanishes if one uses the same regularization prescription that implies the cancellation of the total conformal anomaly a-coefficient. This happens to be true in all even dimensions d >= 2.
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Partition Function of free conformal higher spin theory
Journal of High Energy Physics, 2014Co-Authors: Matteo Beccaria, Xavier Bekaert, Arkady A TseytlinAbstract:We compute the canonical Partition Function Z of non-interacting conformal higher spin (CHS) theory viewed as a collection of free spin s CFT's in R d . We discuss in detail the 4-dimensional case (where s = 1 is the standard Maxwell vector, s = 2 is the Weyl graviton, etc.), but also present a generalization for all even dimensions d. Z may be found by counting the numbers of conformal operators and their descendants (modulo gauge identities and equations of motion) weighted by scaling dimensions. This conformal operator counting method requires a careful analysis of the structure of characters of rele- vant (conserved current, shadow field and conformal Killing tensor) representations of the conformal algebra so(d,2). There is also a close relation to massless higher spin Partition Functions with alternative boundary conditions in AdSd+1. The same Partition Function Z may also be computed from the CHS path integral on a curved S 1 × S d−1 background. This allows us to determine a simple factorized form of the CHS kinetic operator on this conformally flat background. Summing the individual conformal spin contributions Zs over all spins we obtain the total Partition Function of the CHS theory. We also find the corresponding Casimir energy on the sphere and show that it vanishes if one uses the same regularization prescription that implies the cancellation of the total conformal anomaly a-coefficient. This happens to be true in all even dimensionsd ≥ 2.
Xavier Bekaert - One of the best experts on this subject based on the ideXlab platform.
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Partition Function of free conformal higher spin theory
Journal of High Energy Physics, 2014Co-Authors: Xavier Bekaert, Tseytlin Arkady, Matteo BeccariaAbstract:We compute the canonical Partition Function Z of non-interacting conformal higher spin (CHS) theory viewed as a collection of free spin s CFT's in R^d. We discuss in detail the 4-dimensional case (where s=1 is the standard Maxwell vector, s=2 is the Weyl graviton, etc.), but also present a generalization for all even dimensions d. Z may be found by counting the numbers of conformal operators and their descendants (modulo gauge identities and equations of motion) weighted by scaling dimensions. This conformal operator counting method requires a careful analysis of the structure of characters of relevant (conserved current, shadow field and conformal Killing tensor) representations of the conformal algebra so(d,2). There is also a close relation to massless higher spin Partition Functions with alternative boundary conditions in AdS_{d+1}. The same Partition Function Z may also be computed from the CHS path integral on a curved S^1 x S^{d-1} background. This allows us to determine a simple factorized form of the CHS kinetic operator on this conformally flat background. Summing the individual conformal spin contributions Z_s over all spins we obtain the total Partition Function of the CHS theory. We also find the corresponding Casimir energy and show that it vanishes if one uses the same regularization prescription that implies the cancellation of the total conformal anomaly a-coefficient. This happens to be true in all even dimensions d >= 2.
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Partition Function of free conformal higher spin theory
Journal of High Energy Physics, 2014Co-Authors: Matteo Beccaria, Xavier Bekaert, Arkady A TseytlinAbstract:We compute the canonical Partition Function Z of non-interacting conformal higher spin (CHS) theory viewed as a collection of free spin s CFT's in R d . We discuss in detail the 4-dimensional case (where s = 1 is the standard Maxwell vector, s = 2 is the Weyl graviton, etc.), but also present a generalization for all even dimensions d. Z may be found by counting the numbers of conformal operators and their descendants (modulo gauge identities and equations of motion) weighted by scaling dimensions. This conformal operator counting method requires a careful analysis of the structure of characters of rele- vant (conserved current, shadow field and conformal Killing tensor) representations of the conformal algebra so(d,2). There is also a close relation to massless higher spin Partition Functions with alternative boundary conditions in AdSd+1. The same Partition Function Z may also be computed from the CHS path integral on a curved S 1 × S d−1 background. This allows us to determine a simple factorized form of the CHS kinetic operator on this conformally flat background. Summing the individual conformal spin contributions Zs over all spins we obtain the total Partition Function of the CHS theory. We also find the corresponding Casimir energy on the sphere and show that it vanishes if one uses the same regularization prescription that implies the cancellation of the total conformal anomaly a-coefficient. This happens to be true in all even dimensionsd ≥ 2.
Mark Jerrum - One of the best experts on this subject based on the ideXlab platform.
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approximating the Partition Function of planar two state spin systems
Journal of Computer and System Sciences, 2015Co-Authors: Leslie Ann Goldberg, Mark Jerrum, Colin McquillanAbstract:We consider the problem of approximating the Partition Function of the hard-core model on planar graphs of degree at most 4. We show that when the activity λ is sufficiently large, there is no fully polynomial randomised approximation scheme for evaluating the Partition Function unless NP = RP . The result extends to a nearby region of the parameter space in a more general two-state spin system with three parameters. We also give a polynomial-time randomised approximation scheme for the logarithm of the Partition Function. We study approximation of the hard-core Partition Function.Our graphs are planar with degree at most 4.We show that the problem is intractable for sufficiently high activity.However, the logarithm of the Partition Function can be approximated.
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approximating the Partition Function of the ferromagnetic potts model
International Colloquium on Automata Languages and Programming, 2010Co-Authors: Leslie Ann Goldberg, Mark JerrumAbstract:We provide evidence that it is computationally difficult to approximate the Partition Function of the ferromagnetic q-state Potts model when q > 2. Specifically we show that the Partition Function is hard for the complexity class #RHΠ1 under approximation-preserving reducibility. Thus, it is as hard to approximate the Partition Function as it is to find approximate solutions to a wide range of counting problems, including that of determining the number of independent sets in a bipartite graph. Our proof exploits the first order phase transition of the "random cluster" model, which is a probability distribution on graphs that is closely related to the q-state Potts model. A full version of this paper, with proofs included, is available at http://arxiv.org/abs/1002.0986.
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approximating the Partition Function of the ferromagnetic potts model
arXiv: Computational Complexity, 2010Co-Authors: Leslie Ann Goldberg, Mark JerrumAbstract:We provide evidence that it is computationally difficult to approximate the Partition Function of the ferromagnetic q-state Potts model when q>2. Specifically we show that the Partition Function is hard for the complexity class #RHPi_1 under approximation-preserving reducibility. Thus, it is as hard to approximate the Partition Function as it is to find approximate solutions to a wide range of counting problems, including that of determining the number of independent sets in a bipartite graph. Our proof exploits the first order phase transition of the "random cluster" model, which is a probability distribution on graphs that is closely related to the q-state Potts model.
Niles A Pierce - One of the best experts on this subject based on the ideXlab platform.
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a Partition Function algorithm for nucleic acid secondary structure including pseudoknots
Journal of Computational Chemistry, 2003Co-Authors: Robert M Dirks, Niles A PierceAbstract:Nucleic acid secondary structure models usually exclude pseudoknots due to the difficulty of treating these nonnested structures efficiently in structure prediction and Partition Function algorithms. Here, the standard secondary structure energy model is extended to include the most physically relevant pseudoknots. We describe an O(N^5) dynamic programming algorithm, where N is the length of the strand, for computing the Partition Function and minimum energy structure over this class of secondary structures. Hence, it is possible to determine the probability of sampling the lowest energy structure, or any other structure of particular interest. This capability motivates the use of the Partition Function for the design of DNA or RNA molecules for bioengineering applications.
