High precision study of the structure of supersymmetric Yang–Mills quantum mechanics

Abstract

The spectrum of D = 4 supersymmetric Yang-Mills quantum mechanics is computed with high accuracy in all channels of angular momentum and fermion number. Localized and non-localized states coexists in certain channels as a consequence of the supersymmetric interactions with flat valleys. All states fall into well identifiable supermultiplets providing an explicit realization of supersymmetry on the spectroscopic level. An accidental degeneracy among some supermultiplets has been found. Regularized Witten index converges to a time-independent constant which agrees with earlier calculations.

Supersymmetric Yang-Mills quantum mechanics in various dimensions

“…For supersymmetric systems, however, the above fluctuations cancel between fermions and bosons, and the continuous spectrum appears [16]. All these features were observed [11] and confirmed with high accuracy in Refs [13]. Moreover, it was found that the continuum spectrum appears only in certain channels, while the localized states exist for all fermion 1 The number of fermionic quanta is finite in reduced theories.…”

“…In Ref. [13] this was replaced by a fast, recursive calculation of all matrix elements. Where possible conservation laws were used.…”

“…In particular, using this scaling, a dispersion relation for the scattering states was confirmed [17] and obtained for more complicated fermionic sectors. Other results obtained in [13] include study of the restoration of supersymmetry with increasing cutoff and calculation of the Witten index.…”

A method for measuring the Witten index using lattice simulation

“…Related calculations are found in [35,36,37]. For this system, a numerical treatment in the Fock space is proposed [38,39,40,41] which is also useful to obtain the Witten index as well. To the author's best knowledge, however, only a little is known about the index from direct calculations of the quantum mechanics so far.…”

Canonical simulations of supersymmetric SU(N) Yang-Mills quantum mechanics

“…Apart from providing tests of the gauge/gravity duality, SYM quantum mechanics is interesting per se. There are various intriguing expectations concerning the behaviour of the theory in specific sectors of fixed fermion number [1,2]. In particular, while certain canonical sectors only have a discrete energy spectrum, some sectors allow for the discrete spectrum to be immersed in a continuous one reaching down to zero energy.…”