Spectra of supersymmetric Yang-Mills quantum mechanics (original) (raw)
Related papers
2005
Supersymmetric Yang-Mills quantum mechanics (SYMQM) results from the dimensional reduction of the Yang-Mills field theory in D space-time dimensions to a single point in the D − 1 dimensional space. It can be also viewed as the effective quantum mechanics of zero momentum modes of the original theory [1]. These systems were first considered in 80’s [2] as simple models with supersymmetry [3]. Independently, zero-volume field theories (especially pure Yang-Mills) were employed as the starting point of the small volume expansion, which is an important theoretical tool complementary to early lattice calculations [4, 5, 6]. Later the models attracted a new wave of interest after the hypothesis of the equivalence, between the D = 10,SU(∞) SYMQM and a M-theory of D0 branes [7, 8, 9, 10]. In this talk some new results obtained for the D = 4 system with SU(2) gauge symmetry will be presented. PoS(LAT2005)273
Massive super-Yang–Mills quantum mechanics: Classification and the relation to supermembrane
Nuclear Physics B, 2006
We classify the supersymmetric mass deformations of all the super Yang-Mills quantum mechanics, which are obtained by dimensional reductions of minimal super Yang-Mills in spacetime dimensions: ten, six, four, three and two. The resulting actions can be viewed as the matrix descriptions of supermembranes in nontrivial backgrounds of one higher dimensional supergravity theories. We also discuss the utmost generalization of the light-cone formulation of the Nambu-Goto action for a p-brane, including time dependent backgrounds.
On the structure of supersymmetric Yang–Mills quantum mechanics
Physics Letters B, 2005
In ten space-time dimensions the number of Majorana-Weyl fermions is not conserved, not only during the time evolution, but also by rotations. As a consequence the empty Fock state is not rotationally symmetric. We construct explicitly the simplest singlet state which provides the starting point for building up invariant SO(9) subspaces. The state has non-zero fermion number and is a complicated combination of the 1360 elementary, gauge invariant, gluinoless Fock states with twelve fermions. Fermionic structure of higher irreps of SO(9) is also briefly outlined.
Supersymmetric Yang-Mills theories in D ⩾ 12
Nuclear Physics B, 1998
We present supersymmetric Yang-Mills theories in arbitrary even dimensions with the signature (9 + m, 1 + m) where m = 0, 1, 2, • • • beyond ten-dimensions up to infinity. This formulation utilizes null-vectors and is a generalization of our previous work in 10+2 dimensions to arbitrary even dimensions with the above signature. We have overcome the previously-observed obstruction beyond 11+3 dimensions, by the aid of projection operators. Both component and superspace formulations are presented. This also suggests the possibility of consistent supergravity theories in any even dimensions beyond 10+1 dimensions.
Mass spectrum of supersymmetric Yang-Mills theory in three dimensions
Physical Review D, 2000
We consider supersymmetric Yang-Mills theory on R×S 1 ×S 1 . In particular, we choose one of the compact directions to be light-like and another to be space-like. Since the SDLCQ regularization explicitly preserves supersymmetry, this theory is totally finite, and thus we can solve for bound state wave functions and masses numerically without renormalizing. We present the masses as functions of the longitudinal and transverse resolutions and show that the masses converge rapidly in both resolutions. We also study the behavior of the spectrum as a function of the coupling and find that at strong coupling there is a stable, well defined spectrum which we present. We also find several unphysical states that decouple at large transverse resolution. There are two sets of massless states; one set is massless only at zero coupling and the other is massless at all couplings. Together these sets of massless states are in one-to-one correspondence with the full spectrum of the dimensionally reduced theory.
Physical Review D, 2001
We apply supersymmetric discrete light-cone quantization (SDLCQ) to the study of supersymmetric Yang-Mills theory on R × S 1 × S 1. One of the compact directions is chosen to be light-like and the other to be space-like. Since the SDLCQ regularization explicitly preserves supersymmetry, this theory is totally finite, and thus we can solve for bound-state wave functions and masses numerically without renormalizing. We present an overview of all the massive states of this theory, and we see that the spectrum divides into two distinct and disjoint sectors. In one sector the SDLCQ approximation is only valid up to intermediate coupling. There we find a well defined and well behaved set of states, and we present a detailed analysis of these states and their properties. In the other sector, which contains a completely different set of states, we present a much more limited analysis for strong coupling only. We find that, while these state have a well defined spectrum, their masses grow with the transverse momentum cutoff. We present an overview of these states and their properties.
Two-dimensional super Yang-Mills theory investigated with improved resolution
Physical Review D, 2005
In earlier work, N = (1, 1) super Yang-Mills theory in two dimensions was found to have several interesting properties, though these properties could not be investigated in any detail. In this paper we analyze two of these properties. First, we investigate the spectrum of the theory. We calculate the masses of the low-lying states using the supersymmetric discrete light-cone (SDLCQ) approximation and obtain their continuum values. The spectrum exhibits an interesting distribution of masses, which we discuss along with a toy model for this pattern. We also discuss how the average number of partons grows in the bound states. Second, we determine the number of fermions and bosons in the N = (1, 1) and N = (2, 2) theories in each symmetry sector as a function of the resolution. Our finding that the numbers of fermions and bosons in each sector are the same is part of the answer to the question of why the SDLCQ approximation exactly preserves supersymmetry.
Progress in classically solving ten-dimensional supersymmetric reduced Yang-Mills theories
Nuclear Physics B, 1999
It is shown that there exists an on-shell light cone gauge where half of the fermionic components of the super vector potential vanish, so that part of the superspace flatness conditions becomes linear. After reduction to (1+ 1) space-time dimensions, the general solution of this subset of equations is derived. The remaining non-linear equations are written in a form which is analogous to Yang equations, albeit with superderivatives involving sixteen fermionic coordinates. It is shown that this non-linear part may, nevertheless, be solved by methods similar to powerful technics previously developed for the (purely bosonic) self-dual Yang Mills equations in four dimensions.
One dimensional supersymmetric Yang- Mills theory with 16 supercharges
Proceedings of The 30th International Symposium on Lattice Field Theory — PoS(Lattice 2012), 2012
We report on numerical simulations of one dimensional maximally supersymmetric SU(N) Yang-Mills theory, by using the lattice action with two exact supercharges. Based on the gauge/gravity duality, the gauge theory corresponds to N D0-branes system in type IIA superstring theory at finite temperature. We aim to verify the gauge/gravity duality numerically by comparing our results of the gauge side with analytic solutions of the gravity side. First of all, by examining the supersymmetric Ward-Takahashi relation, we show that supersymmetry breaking effects from the cutoff vanish in the continuum limit and our lattice theory has the desired continuum limit. Then, we find that, at low temperature, the black hole internal energy obtained from our data is close to the analytic solution of the gravity side. It suggests the validity of the duality.
Supersymmetric structures in 4-D Yang–Mills theory
The European Physical Journal C, 1998
Recently there has been much progress in understanding confinement in the N=2 supersymmetric Yang-Mills theory. Here we shall investigate how these results could be extended to explain color confinement in the ordinary Yang-Mills theory. In particular, we inquire whether confinement in the N=2 theory can be related to color confinement in the ordinary Yang-Mills theory in the framework of Parisi-Sourlas dimensional reduction. For this we study the partition function of the ordinary Yang-Mills theory in different regimes. Our analysis reveals that an intimate connection indeed exists between these two approaches.