Non-commutative solitons

By Rajesh Gopakumar, Shiraz Minwalla, Andrew Strominger. 2000

392 citations recorded by the source corpus.

We nd classically stable solitons (instantons) in odd (even) dimen- sional scalar non-commutative eld theories whose scalar potential, V(), has at least two minima. These solutions are bubbles of the false vacuum whose size is set bythescaleofnoncommutativity. Ourconstructionusesthecorrespondencebetween non-commutativeelds and operators on a single particle Hilbert space. In the case of non-commutative gauge theories we note that expanding around a simple solu- tion shifts away the kinetic term and results in a purely quartic action with linearly realised gauge symmetries.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/0cd28c2facadd8944fe462f7c6e5cf9877beaba8

How researchers see this paper

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In Astronomy and Astrophysics

1. Ashoke Sen
2. L. Rastelli
3. B. Zwiebach
4. Per Kraus
5. E. Witten
6. S. Giombi
7. Rajesh Gopakumar
8. N. Seiberg

In Nuclear and High Energy Physics

1. Ashoke Sen
2. L. Rastelli
3. E. Witten
4. B. Zwiebach
5. J. Maldacena
6. Per Kraus
7. N. Seiberg
8. Marcos Mariño

In Statistical and Nonlinear Physics

1. Ashoke Sen
2. L. Rastelli
3. B. Zwiebach
4. Marcos Mariño
5. E. Witten
6. Michael R Douglas
7. Per Kraus
8. N. Nekrasov

Citations in the corpus

• Minimal Length Scale Scenarios for Quantum Gravity (2012, background): “Gaussian distributions are of interest not only because they are widely used field configurations, but, for example, also because they may describe solitonic solutions in a potential [137].”
• Conformal higher spin symmetries of 4D massless supermultiplets and osp(L,2M) invariant equations in generalized (super)space (2001, neutral): “ with the one-particle states of the same system [19]. (Note thatthese Fock modules are somewhat reminiscent of the modules introduced for the description of non-commutative solitons in string theory [28].) In addition to the su(2,2|N) generators, the algebra hu(2N−1,2N−1|8) contains the bilinear ge”
• A Review on Tachyon Condensation in Open String Field Theories (2001, positive): “It was shown in [101, 104] that the operator |n〉〈n| corresponds to the function (field) φn(r (2)) = 2(−1)ne− r 2 θ Ln ( 2r(2) θ ) , (6.”
• D-branes and strings as non-commutative solitons (2000, methodology): “22) represents, in the basis constructed in [17], a lump of size rk ∼ √ k, which approximates the string field configuration of an unstable D25-brane for smaller radius, and the closed string vacuum state for larger radius.”
• Noncommutative Tachyons And String Field Theory (2000, background): “Recently, solitons in scalar field theories on noncommutative spacetimes with very large noncommutativity parameter θ have been constructed in a strikingly simple way [1].”
• Half-strings, projectors and multiple D-branes (2001, result): “This situation is analogous to the one that arises in the study of non-commutative solitons [8, 9, 10, 11, 12].”
• Unstable solitons in noncommutative gauge theory (2000, background): “We find exact classical solutions which carry various kinds of fluxes but, as in [2], are not, in general, BPS (in contrast to the gauge theory solutions in [1]).”
• A Note on Background Independence in Noncommutative Gauge Theories, Matrix Model and Tachyon Condensation (2000, background): “(A connection between the matrix model and this problem was anticipated in [12,32].”
• Classical solutions in string field theory around the tachyon vacuum (2001, methodology): “(This is precisely what happens in the case of p-adic string theory [29, 30, 31], background independent open string field theory [32, 33, 34, 35, 36, 37, 38, 39, 40], as well as non-commutative solitons [41, 42, 43].”
• String Field Theory Around the Tachyon Vacuum (2000, methodology): “Support for these conjectures comes from the analysis of the world-sheet theory [1, 3, 4, 5, 6, 7, 8], cubic open string field theory [9, 10, 11, 12, 13, 14, 15, 16, 17, 19, 20, 21, 22, 23, 24], noncommutative limit of the effective field theory of the tachyon [25, 26, 27, 28, 29, 30], background in”
• Remarks on Tachyon Condensation in Superstring Field Theory (2000, result): “Exact results for tachyon condensation have also been obtained by introducing noncommutativity [16,17,18,19]; the recent results of [20] might give a closer relation between this approach and BSFT.”
• Exact Solution of Quantum Field Theory on Noncommutative Phase Spaces (2003, background): “The corresponding field configurations correspond to the standard θ = ∞ GMS solitons [40] and possess an infinite degeneracy under U(∞) rotations of the matrices X, leading to a non-trivial soliton moduli space which is an infinite-dimensional Grassmannian [41].”
• Chern–Simons theory with vector fermion matter (2011, background): “Also, it naturally appears in discussions of non-commutative field theory [48], [49], [50].”
• Phase structure of non-commutative scalar field theories (2000, background): “ar X iv :h ep -t h/ 00 W e investigate the phase structure ofnon-com m utative scalar eld theoriesand nd evidence forordered phaseswhich break translation invariance.”
• Quantum field theory on noncommutative spaces (2001, background): “table noncommutative solitons, which have no counterparts in ordinary field theory, have been constructed by representing the Weyl operator algebra on a multi-particle quantum mechanical Hilbert space [64, 65]. The noncommutative soliton field equations may then be solved by any projection operator on”
• Noncommutative field theory (2001, methodology): “This argument will obviously fail in the presence of a distinguished length scale √ θ and in fact one finds that for sufficiently large θ, stable solitons can exist in the noncommutative theory (Gopakumar, Minwalla, and Strominger 2000c).”