Zihan Wang (Imperial College) - Energy of wrapped M2 branes at higher loops

by Zihan Wang (Imperial College London)

Wednesday 2 Sept 2026, 15:00 → 16:00 Europe/Stockholm

92110 (Ångströmlaboratoriet)

The static-gauge Green–Schwarz strings and supermembranes are formally non-renormalizable. Some quantities may still be free of logarithmic UV divergences and thus be defined unambiguously. One example is the energy of an M2 brane wrapping one or two compact directions in a flat background. For an M2 brane wrapped on a two-torus, the one- and two-loop corrections are free of logarithmic UV divergences and are well defined using zeta-function regularization. With periodic fermions, the quantum corrections cancel, as expected from supersymmetry, whereas antiperiodic boundary conditions lead to non-trivial functions of the compactification radii involving modified Bessel functions. In the string case, the static-gauge loop expansion reproduces the expansion of the exact square-root spectrum. At three loops, however, the membrane displays new structure: in addition to powers of the one-loop zeta(3) coefficient, the basketball diagram generates a new zeta(9) term. The leading large-N bubble diagrams can nevertheless be resummed: they give the quadratic equation and square-root energy for the string, but a cubic equation for the membrane. We find that the bubble-graph part of the membrane energy does not vanish for any value of the radius R_{11}. We also generalize the two-loop analysis to an M2 brane in a flat eleven-dimensional “twisted” background that interpolates between periodic and antiperiodic fermion boundary conditions.