On some special cases of Gaiotto’s positivity conjecture. (English) Zbl 07912350
Summary: We prove a conjecture of D. Gaiotto on positivity of inner products arising in studying Landau-Ginzburg boundary conditions in the 1-dimensional case, and in special cases in higher dimensions, for 3d free hypermultiplets.
MSC:
| 81T13 | Yang-Mills and other gauge theories in quantum field theory |
| 42A82 | Positive definite functions in one variable harmonic analysis |
| 15B48 | Positive matrices and their generalizations; cones of matrices |
References:
| [1] | Gaiotto, D., Sphere quantization of {H}iggs and {C}oulomb branches and analytic symplectic duality |
| [2] | Gantmacher, F. R., The theory of matrices, {V}ol. 2, ix+276, (1959), Chelsea Publishing Co., New York · Zbl 0085.01001 |
| [3] | Gr\"ochenig, Karlheinz, Schoenberg’s theory of totally positive functions and the {R}iemann zeta function, Sampling, {A}pproximation, and {S}ignal {A}nalysis. {H}armonic {A}nalysis in the {S}pirit of {J}. {R}owland {H}iggins, Appl. Numer. Harmon. Anal., 193-210, (2023), Birkh\"auser, Cham · Zbl 07916535 · doi:10.1007/978-3-031-41130-4_9 |
| [4] | Karlin, Samuel, Total positivity. {V}ol. {I}, xii+576, (1968), Stanford University Press, Stanford, CA · Zbl 0219.47030 |
| [5] | Karlin, Samuel, Total positivity, absorption probabilities and applications, Transactions of the American Mathematical Society, 111, 33-107, (1964) · Zbl 0122.13702 · doi:10.2307/1993667 |
| [6] | Rid, M. and Simon, B., Methods of modern mathematical physics, {Vo}l. {II}, (1975), Academic Press, New York · Zbl 0308.47002 |
| [7] | Schoenberg, I. J., On {P}\'olya frequency functions. {I}. {T}he totally positive functions and their {L}aplace transforms, Journal d’Analyse Math\'ematique, 1, 331-374, (1951) · Zbl 0045.37602 · doi:10.1007/BF02790092 |
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