| 1. |
- Basso, Benjamin, et al.
(författare)
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Structure Constants of Short Operators in Planar N=4 Supersymmetric Yang-Mills Theory
- 2023
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Ingår i: Physical Review Letters. - : American Physical Society (APS). - 0031-9007 .- 1079-7114. ; 130:13
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Tidskriftsartikel (refereegranskat)abstract
- We present a conjecture for the three-point functions of single-trace operators in planar N = 4 super -Yang-Mills theory at finite coupling, in the case where two operators are protected. Our proposal is based on the hexagon representation for structure constants of long operators, which we complete to incorporate operators of any length using data from the TBA-QSC formalism. We perform various tests of our conjecture, at weak and strong coupling, finding agreement with the gauge theory through 5 loops for the shortest three-point function and with string theory in the classical limit.
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| 2. |
- Bendle, Dominik, et al.
(författare)
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Integration-by-parts reductions of Feynman integrals using Singular and GPI-Space
- 2020
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Ingår i: Journal of High Energy Physics (JHEP). - : SPRINGER. - 1126-6708 .- 1029-8479. ; :2
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Tidskriftsartikel (refereegranskat)abstract
- We introduce an algebro-geometrically motived integration-by-parts (IBP) re- duction method for multi-loop and multi-scale Feynman integrals, using a framework for massively parallel computations in computer algebra. This framework combines the com- puter algebra system Singular with the workflow management system GPI-Space, which are being developed at the TU Kaiserslautern and the Fraunhofer Institute for Industrial Mathematics (ITWM), respectively. In our approach, the IBP relations are first trimmed by modern tools from computational algebraic geometry and then solved by sparse linear algebra and our new interpolation method. Modelled in terms of Petri nets, these steps are efficiently automatized and automatically parallelized by GPI-Space. We demonstrate the potential of our method at the nontrivial example of reducing two-loop five-point non- planar double-pentagon integrals. We also use GPI-Space to convert the basis of IBP reductions, and discuss the possible simplification of master-integral coefficients in a uni- formly transcendental basis.
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| 3. |
- Bissi, Agnese, et al.
(författare)
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All loop structures in supergravity amplitudes on AdS(5) x S-5 from CFT
- 2021
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Ingår i: Journal of Physics A. - : Institute of Physics Publishing (IOPP). - 1751-8113 .- 1751-8121. ; 54:32
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Tidskriftsartikel (refereegranskat)abstract
- We compute a set of structures which appear in the four-point function of protected operators of dimension two in N = 4 super Yang Mills with SU(N) gauge group, at any order in a large N expansion. They are determined only by leading order CFT data. By focusing on a specific limit, we make connection with the dual supergravity amplitude in flat space, where such structures correspond to iterated s-cuts. We make several checks and we conjecture that the same interpretation holds for supergravity amplitudes on AdS(5) x S-5.
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| 4. |
- Bissi, Agnese, et al.
(författare)
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Towards all loop supergravity amplitudes on AdS5 x S5
- 2021
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Ingår i: Physical Review D. - : American Physical Society. - 2470-0010 .- 2470-0029. ; 104:4
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Tidskriftsartikel (refereegranskat)abstract
- We study the four-point function of the superconformal primary of the stress-tensor multiplet in fourdimensional N = 4 super Yang-Mills theory, at strong coupling and in a large-N expansion. This observable is holographically dual to a four-graviton amplitude in type IIB supergravity on AdS(5) x S-5 . We construct the maximal transcendental weight piece of the correlator at order N-6 and compare it with the flat-space limit of the corresponding two-loop amplitude. This allows us to conjecture structures of the correlator/amplitude which should be present at any loop order.
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| 5. |
- Boehm, Janko, et al.
(författare)
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Complete sets of logarithmic vector fields for integration-by-parts identities of Feynman integrals
- 2018
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Ingår i: Physical Review D. - 2470-0010 .- 2470-0029. ; 98:2
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Tidskriftsartikel (refereegranskat)abstract
- Integration-by-parts identities between loop integrals arise from the vanishing integration of total derivatives in dimensional regularization. Generic choices of total derivatives in the Baikov or parametric representations lead to identities which involve dimension shifts. These dimension shifts can be avoided by imposing a certain constraint on the total derivatives. The solutions of this constraint turn out to be a specific type of syzygies which correspond to logarithmic vector fields along the Gram determinant formed of the independent external and loop momenta. We present an explicit generating set of solutions in Baikov representation, valid for any number of loops and external momenta, obtained from the Laplace expansion of the Gram determinant. We provide a rigorous mathematical proof that this set of solutions is complete. This proof relates the logarithmic vector fields in question to ideals of submaximal minors of the Gram matrix and makes use of classical resolutions of such ideals.
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| 6. |
- Böhm, Janko, et al.
(författare)
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Complete integration-by-parts reductions of the non-planar hexagon-box via module intersections
- 2018
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Ingår i: Journal of High Energy Physics (JHEP). - : SPRINGER. - 1126-6708 .- 1029-8479. ; :9
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Tidskriftsartikel (refereegranskat)abstract
- We present the powerful module-intersection integration-by-parts (IBP) method, suitable for multi-loop and multi-scale Feynman integral reduction. Utilizing modern computational algebraic geometry techniques, this new method successfully trims traditional IBP systems dramatically to much simpler integral-relation systems on unitarity cuts. We demonstrate the power of this method by explicitly carrying out the complete analytic reduction of two-loop five-point non-planar hexagon-box integrals, with degree-four numerators, to a basis of 73 master integrals.
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| 7. |
- Chicherin, Dmitry, et al.
(författare)
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All five-loop planar four-point functions of half-BPS operators in N = 4 SYM
- 2018
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Ingår i: Journal of High Energy Physics (JHEP). - 1126-6708 .- 1029-8479. ; 11, s. 1-26
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Tidskriftsartikel (refereegranskat)abstract
- We obtain all planar four-point correlators of half-BPS operators in N = 4 SYM up to five loops. The ansatz for the integrand is fixed partially by imposing lightcone OPE relations between different correlators. We then fix the integrated correlators by comparing their asymptotic expansions with simple data obtained from integrability. We extract OPE coefficients and find a prediction for the triple wrapping correction of the hexagon form factors, which contributes already at the five-loop order.
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| 8. |
- Córdova, Lucía, et al.
(författare)
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The O(N) monolith reloaded: sum rules and Form Factor Bootstrap
- 2024
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Ingår i: Journal of High Energy Physics (JHEP). - : Springer Nature. - 1126-6708 .- 1029-8479. ; 2024:1
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Tidskriftsartikel (refereegranskat)abstract
- We revisit the space of gapped quantum field theories with a global O(N) symmetry in two spacetime dimensions. Previous works using S-matrix bootstrap revealed a rich space in which integrable theories such as the non-linear sigma model appear at special points on the boundary, along with an abundance of unknown models hinting at a non conventional UV behaviour. We extend the S-matrix set-up by including into the bootstrap form factors and spectral functions for the stress-energy tensor and conserved O(N) currents. Sum rules allow us to put bounds on the central charges of the conformal field theory (CFT) in the UV. We find that a big portion of the boundary can only flow from CFTs with infinite central charges. We track this result down to a particular behaviour of the amplitudes in physical kinematics and discuss its physical implications.
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| 9. |
- Georgoudis, Alessandro, et al.
(författare)
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AZURITE : An algebraic geometry based package for finding bases of loop integrals
- 2017
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Ingår i: Computer Physics Communications. - : Elsevier BV. - 0010-4655 .- 1879-2944. ; 221, s. 203-215
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Tidskriftsartikel (refereegranskat)abstract
- For any given Feynman graph, the set of integrals with all possible powers of the propagators spans a vector space of finite dimension. We introduce the package AZURITE (A ZURich-bred method for finding master InTEgrals), which efficiently finds a basis of this vector space. It constructs the needed integration by-parts (IBP) identities on a set of generalized-unitarity cuts. It is based on syzygy computations and analyses of the symmetries of the involved Feynman diagrams and is powered by the computer algebra systems SINGULAR and MATHEMATICA. It can moreover analytically calculate the part of the IBP identities that is supported on the cuts. In some cases, the basis obtained by AZURITE may be slightly overcomplete.Program summaryProgram Title: AZURITELicensing provisions: GNU General Public License (GPL)Programming language: Wolfram MATHEMATICA version 10.0 or higherSupplementary material: A manual in the form of a MATHEMATICA notebookNature of problem: Determination of a basis of the space of loop integrals spanned by a given Feynman diagram and all of its subdiagramsSolution method: MATHEMATICA implementation.
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| 10. |
- Georgoudis, Alessandro, et al.
(författare)
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Five-loop massless propagator integrals
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Annan publikation (övrigt vetenskapligt/konstnärligt)abstract
- We develop a method to obtain ϵ-expansions of massless two-point integrals in position space, based on the constraints implied by symmetries of the asymptotic expansion of conformal four-point integrals. Together with parametric integration, we are able to fix the expansions of 170 genuine five-loop master integrals. In particular, we computed the expansions of all planar master integrals up to transcendental weight 9.
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