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Keywords
(11)
adscft correspondence
Continuous Spectrum
Integrable Field Theories
Moduli Space
Quantum Mechanics
Soliton Solution
Solitons Monopoles and Instantons
Symmetric Space
Symmetry Group
Sine Gordon
Time Dependent
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Classical and quantum solitons in the symmetric space sineGordon theories
Classical and quantum solitons in the symmetric space sineGordon theories,10.1007/JHEP04(2011)119,Journal of High Energy Physics,Timothy J. Hollowood
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Classical and quantum solitons in the symmetric space sineGordon theories
(
Citations: 3
)
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Timothy J. Hollowood
,
J. Luis Miramontes
We construct the soliton solutions in the
symmetric space
sineGordon theories. The latter are a series of
integrable field theories
in 1 + 1dimensions which are associated to a
symmetric space
F/G, and are related via the Pohlmeyer reduction to theories of strings moving on symmetric spaces. We show that the solitons are kinks that carry an internal
moduli space
that can be identified with a particular coadjoint orbit of the unbroken subgroup H ⊂ G. Classically the solitons come in a
continuous spectrum
which encompasses the perturbative fluctuations of the theory as the kink charge becomes small. We show that the solitons can be quantized by allowing the collective coordinates to be timedependent to yield a form of
quantum mechanics
on the coadjoint orbit. The quantum states correspond to symmetric tensor representations of the
symmetry group
H and have the interpretation of a fuzzy geometric version of the coadjoint orbit. The quantized finite tower of soliton states includes the perturbative modes at the base.
Journal:
Journal of High Energy Physics  J HIGH ENERGY PHYS
, vol. 2011, no. 4, pp. 150, 2011
DOI:
10.1007/JHEP04(2011)119
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Citation Context
(3)
...The construction here generalizes the same analysis for the ordinary, or bosonic, SSSG theories that appears in the companion papers [
24
, 25]...
...We then go on, following the companion paper [
24
], to construct soliton solutions in the SSSSG theories using the dressing method...
...In the final section, we proceed, once again following [
24
, 25], to a semiclassical quantization of the solitons by quantizing their moduli space dynamics...
...An important feature of these theories is that they admit soliton solutions whose fields do not falloff at x = ±∞, and it was emphasized in [
24
, 25] that this makes the WZ term require careful treatment...
...Writing γ = e φ , the true Noether current is [
24
, 25]...
...It follows that the “subtracted monodromy” [
24
]...
...However, at the next level STr(�h±2,�) give the components of the energymomentum tensor, much as in the bosonic theories [
24
],...
...The idea will be to generalize the dressing method used in the bosonic theories and described in detail in [
24
]...
...The key to solving them is to propose that the residues have rank one [
24
, 40]:...
...This matches the mass calculated in the bosonic SSSG theories in [
24
]...
...X. However, as was shown in [
24
, 25], for the SSSG theories the dominant terms are actually linear in ú...
...In fact, it was found in [
24
] that this picture can be made very concrete: the semiclassical soliton states are coherent states of high excitation number of order k. In contrast, for the Grassmann odd sector these kind of semiclassical states do not exist, and because of Fermi statistics there are only a small number of states with low occupation number...
...First of all, we consider the bosonic solution with all the Grassmann odd coordinates turned off u± = 0. In this case, following the discussion in [
24
, 25], the moduli space in the Grassmann even directions takes the form of a coadjoint orbit of the subgroup Hb = SU(2) + ×SU(2) − ⊂ H. In order to find the effective quantum mechanical action, we...
...It is important to notice that this is not a gauge transformation since we keep A� = 0. In [
24
], it was proved that the effective action for U(t) is...
Timothy J. Hollowood
,
et al.
The AdS 5 × S 5 semisymmetric space sineGordon theory
...(R) − were termed as “missing” in [
8
]. They do not appear explicitly in the final form of L±...
...Fortunately, this can be done by extending to the supersymmetric case, the results recently presented in [
17
] for the bosonic symmetricspace sineGordon models...
David M. Schmidtt
,
et al.
Supersymmetry flows, semisymmetric space sineGordon models and the P...
...In this note we summarize some recent progress in understanding the SSSG theories and their relation to the string sigma models [
29
]...
...main paper [
29
] describes the generalization to any Symmetric Space of Type I in Cartan’s classification...
...expansion. We can write the effective description in terms of a timedependent symmetry transformation of the static solution U(t), in the form [
29
] 8...
...Then, as q → 0, the mass of the kink goes to 0 as ℓ → 0 and so solitons with small charge are not bonafide semiclassical objects; rather they are actually the perturbative excitations of the theory [
29
]...
...For the Qball kinks of the SSSG theory this was shown in [
29
] with the result...
...The states at the bottom of the tower N = 1, which transform in the vector representation of SO(4), correspond to the perturbative excitations of the SSSG Lagrangian [
29
]...
...with the SSSG dressing formalism described in detail in [
29
] and summarized in section 2. Quantities in the sigma model dressing formalism, if denoted with the same letter as in the SSSG formalism, will be highlighted with a tilde...
Timothy J. Hollowood
,
et al.
The semiclassical spectrum of solitons and giant magnons
References
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Journal:
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Andrei Mikhailov
Journal:
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, vol. 56, no. 12, pp. 24292445, 2006
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Andrei Mikhailov
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Pohlmeyer reduction of AdS_5 x S^5 superstring sigma model
(
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M. Grigoriev
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Journal:
Nuclear Physics B  NUCL PHYS B
, 2007
Sort by:
Citations
(3)
The AdS 5 × S 5 semisymmetric space sineGordon theory
(
Citations: 3
)
Timothy J. Hollowood
,
J. Luis Miramontes
Journal:
Journal of High Energy Physics  J HIGH ENERGY PHYS
, vol. 2011, no. 5, pp. 134, 2011
Supersymmetry flows, semisymmetric space sineGordon models and the Pohlmeyer reduction
(
Citations: 2
)
David M. Schmidtt
,
Bento Teobaldo Ferraz
Journal:
Journal of High Energy Physics  J HIGH ENERGY PHYS
, vol. 2011, no. 3, pp. 159, 2011
The semiclassical spectrum of solitons and giant magnons
Timothy J. Hollowood
,
J. Luis Miramontes
Journal:
Journal of High Energy Physics  J HIGH ENERGY PHYS
, vol. 2011, no. 5, pp. 124, 2011