321 research outputs found

### Supersymmetric field theory with benign ghosts

We construct a supersymmetric (1+1)-dimensional field theory involving extra
derivatives and associated ghosts: the spectrum of the Hamiltonian is not
bounded from below, neither from above. In spite of that, there is neither
classical, nor quantum collapse and unitarity is preserved.Comment: Final version published in J.Phys. A; 8 pages, 3 figure

### 6D superconformal theory as the theory of everything

We argue that the fundamental Theory of Everything is a conventional field
theory defined in the flat multidimensional bulk. Our Universe should be
obtained as a 3-brane classical solution in this theory. The renormalizability
of the fundamental theory implies that it involves higher derivatives (HD). It
should be supersymmetric (otherwise one cannot get rid of the huge induced
cosmological term) and probably conformal (otherwise one can hardly cope with
the problem of ghosts) . We present arguments that in conformal HD theories the
ghosts (which are inherent for HD theories) might be not so malignant. In
particular, we present a nontrivial QM HD model where ghosts are absent and the
spectrum has a well defined ground state. The requirement of superconformal
invariance restricts the dimension of the bulk to be D < 7. We suggest that the
TOE lives in six dimensions and enjoys the maximum N = (2,0) superconformal
symmetry. Unfortunately, no renormalizable field theory with this symmetry is
presently known. We construct and discuss an N = (1,0) 6D supersymmetric gauge
theory with four derivatives in the action. This theory involves a
dimensionless coupling constant and is renormalizable. At the tree level, the
theory enjoys conformal symmetry, but the latter is broken by quantum anomaly.
The sign of the beta function corresponds to the Landau zero situation.Comment: 15 pages, 2 figures, based on the talks in Gribov-75 memorial
workshop (Budapest, May 22-24) and the workshop "Supersymmetry and quantum
symmetries" (Dubna, July 27-31

### Multidimensional Dirac strings and the Witten index of SYMCS theories with groups of higher rank

We discuss generalized Dirac strings associated with a given Lie group. They
live in r-dimensional complex space (r being the rank of the group). Such
strings show up in the effective Born-Oppenheimer Hamiltonian for 3d
supersymmetric Yang-Mills-Chern-Simons theories, brought up by the gluon loops.
We calculate accurately the number of the vacuum states in the effective
Hamiltonian associated with these strings. We also show that these states are
irrelevant for the final SYMCS vacuum counting. The Witten index of SYMCS
theories depends thus only on the strings generated by fermion loops and
carrying fractional generalized fluxes.Comment: 34 pages, 4 figure

### Witten index in N=1 and N=2 SYMCS theories with matter

We calculate the Witten index for 3d supersymmetric Yang-Mills-Chern-Simons
theories with matter. For N=2 theories, our results coincide with the results
of recent [1]. We compare the situation in 3d to that in 4d N = 1 theories with
massive matter. In both cases, extra Higgs vacuum states may appear when the
Lagrangian involves nontrivial Yukawa interactions between the matter
superfields. In addition, in 3d theories, massive fermion loops affect the
index via renormalization of the Chern-Simons level k.Comment: 25 pages, 2 figures. Final version published in Nucl. Phys.

### Low--dimensional sisters of Seiberg-Witten effective theory

We consider the theories obtained by dimensional reduction to D=1,2,3 of 4D
supersymmetric Yang--Mills theories and calculate there the effective
low-energy lagrangia describing moduli space dynamics -- the low-dimensional
analogs of the Seiberg--Witten effective lagrangian. The effective theories
thus obtained are rather beautiful and interesting from mathematical viewpoint.
In addition, their study allows one to understand better some essential
features of 4D supersymmetric theories, in particular -- the nonrenormalisation
theorems.Comment: 39 pages. A contribution to Ian Kogan memorial volume. Minor
corrections, a reference adde

### Vacuum structure in supersymmetric Yang-Mills theories with any gauge group

We consider the pure supersymmetric Yang--Mills theories placed on a small
3-dimensional spatial torus with higher orthogonal and exceptional gauge
groups. The problem of constructing the quantum vacuum states is reduced to a
pure mathematical problem of classifying the flat connections on 3-torus. The
latter problem is equivalent to the problem of classification of commuting
triples of elements in a connected simply connected compact Lie group which is
solved in this paper. In particular, we show that for higher orthogonal SO(N),
N > 6, and for all exceptional groups the moduli space of flat connections
involves several distinct connected components. The total number of
vacuumstates is given in all cases by the dual Coxeter number of the group
which agrees with the result obtained earlier with the instanton technique.Comment: 41 pages, 9 figures, 9 tables. Final version to be published in the
Yuri Golfand memorial volume. We added the Appendix D with classification of
all non-trivial commuting n-tuples for arbitrary

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