2016/11/30 by Edi Gava, E. Gava, K. S. Narain +5
Mathematics · Physics and Astronomy · #Applied mathematics #Black Holes and Theoretical Physics #Boundary value problem #Dirichlet distribution #Eigenvalues and eigenvectors #Gauge (firearms) #Gauge theory #Harmonics #Kernel (algebra) #Mathematical analysis #Mathematical physics #Mathematics #Particle physics theoretical and experimental studies #Physics #Pure mathematics #Quantum Chromodynamics and Particle Interactions #Quantum mechanics #hep-th
paper · pdf · doi:10.1016/j.nuclphysb.2017.04.007
47 pages, discussion on instanton corrections in section 6 revised, typos corrected, two references added
openalex publication_date 2017/04/11 · arxiv created 2017/08/14 · arxiv updated 2017/08/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Using localization techniques, we compute the path integral of N=2 SUSY gauge theory coupled to matter on the hemisphere HS4, with either Dirichlet or Neumann supersymmetric boundary conditions. The resulting quantities are wave-functions of the theory depending on the boundary data. The one-loop determinants are computed using SO(4) harmonics basis. We solve kernel and co-kernel equations for the relevant differential operators arising from gauge and matter localizing actions. The second method utilizes full SO(5) harmonics to reduce the computation to evaluating QSUSY2 eigenvalues and its multiplicities. In the Dirichlet case, we show how to glue two wave-functions to get back the partition function of round S4. We will also describe how to obtain the same results using SO(5) harmonics basis.