18,854 research outputs found
No saturation of the quantum Bogomolnyi bound by two-dimensional supersymmetric solitons
We reanalyse the question whether the quantum Bogomolnyi bound is saturated
in the two-dimensional supersymmetric kink and sine-Gordon models. Our starting
point is the usual expression for the one-loop correction to the mass of a
soliton in terms of sums over zero-point energies. To regulate these sums, most
authors put the system in a box with suitable boundary conditions, and impose
an ultraviolet cut-off. We distinguish between an energy cut-off and a mode
number cut-off, and show that they lead to different results. We claim that
only the mode cut-off yields correct results, and only if one considers exactly
the same number of bosonic and fermionic modes in the total sum over
bound-state and zero-point energies. To substantiate this claim, we show that
in the sine-Gordon model only the mode cut-off yields a result for the quantum
soliton mass that is consistent with the exact result for the spectrum as
obtained by Dashen et al. from quantising the so-called breather solution. In
the supersymmetric case, our conclusion is that contrary to previous claims the
quantum Bogomolnyi bound is not saturated in any of the two-dimensional models
considered.Comment: 23 pages, LATe
ABJM on ellipsoid and topological strings
It is known that the large N expansion of the partition function in ABJM
theory on a three-sphere is completely determined by the topological string on
local Hirzebruch surface F_0. In this note, we investigate the ABJM partition
function on an ellipsoid, which has a conventional deformation parameter b.
Using 3d mirror symmetry, we find a remarkable relation between the ellipsoid
partition function for b^2=3 (or b^2=1/3) in ABJM theory at k=1 and a matrix
model for the topological string on another Calabi-Yau threefold, known as
local P^2. As in the case of b=1, we can compute the full large N expansion of
the partition function in this case. This is the first example of the complete
large N solution in ABJM theory on the squashed sphere. Using the obtained
results, we also analyze the supersymmetric Renyi entropy.Comment: 29 page
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