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Michael C. Abbott

Publications and source records attributed to Michael C. Abbott.

30 records · Page 2Linked to original sources
arXiv2013

Meromorphic Functions and the Topology of Giant Gravitons

Using Mikhailov's map from holomorphic functions to supersymmetric D3-brane solutions, we show how to construct giant gravitons in AdS5 x S5 with toroidal topologies. In the 1/4-BPS sector we show that these are always of the form #^K (S2 x S1), and in the limit in which this becomes a set of m+n perpendicular spherical giants re-connected near to their intersections, we find K in terms of m,n. In the 1/8-BPS sector we find a similar class of solutions.

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arXiv2013

Scattering in AdS(2)/CFT(1) and the BES Phase

We study worldsheet scattering for the type IIA superstring in AdS(2) x S(2) x T(6). Using the Green--Schwarz action to quartic order in fermions we take the near-BMN limit, where as in the AdS(3)/CFT(2) case there are both massive and massless excitations. For the massive excitations we compute all possible tree-level processes, and show that these agree with a truncated version of the exact AdS(5) x S(5) S-matrix. We also compute several S-matrix elements involving massless excitations. At one loop we find that the dressing phase is the same Hernandes-Lopez phase appearing in AdS(5)/CFT(4). We see the same phase when calculating this by semiclassical means using the PSU(1,1|2)/U(1)^2 coset sigma model, for which we can also study the scattering of fermions. This supports the conjecture that the all-loop dressing phase is again the BES phase, rather than a new phase like that seen in AdS(3)/CFT(2).

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arXiv2013

The AdS3 x S3 x S3 x S1 Hernandez-Lopez Phases: a Semiclassical Derivation

This note calculates the Hernandez-Lopez phases for strings in AdS3 x S3 x S3 x S1 by semiclassical methods using the d(2,1;α)^2 algebraic curve. By working at general α we include modes absent from previous semiclassical calculations of this phase in AdS3 x S3 x T4, and in particular can study the scattering of particles of different mass. By carefully re-deriving the semiclassical formula we clarify some issues of antisymmetrisation, cutoffs and surface terms which could safely be ignored in AdS5 x S5, and some issues about the terms c_1,s which were absent there. As a result we see agreement with the recently calculated all-loop dressing phase in the AdS3 x S3 x T4 case, and exactly 1/2 this in the general case AdS3 x S3 x S3 x S1 for any α and any (light) polarisations.

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arXiv2013

Comment on Strings in AdS3 x S3 x S3 x S1 at One Loop

This paper studies semiclassical strings in AdS3 x S3 x S3 x S1 using the algebraic curve. Calculating one-loop corrections to the energy of the giant magnon fixes the constant term c in the expansion of the coupling h(λ). Comparing these to similar corrections for long spinning strings gives a prediction for the one-loop term f_1 in the expansion of the cusp anomalous dimension f(h), for all α(where α--> 1 is the AdS3 x S3 x T4 limit). For these semiclassical mode sums there is a similar choice of regularisation prescriptions to that encountered in AdS4 x CP3. However at α\neq 1/2 they lead to different values of f_1 and are therefore not related by a simple change of the coupling. The algebraic curve is also used to calculate various finite-size corrections for giant magnons, which are well-behaved as α--> 1, and can be compared to the recently published S-matrices.

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arXiv2012

Real and Virtual Bound States in Lüscher Corrections for CP3 Magnons

We study classical and quantum finite-size corrections to giant magnons in AdS_4 x CP^3 using generalised Lüscher formulae. Lüscher F-terms are organised in powers of the exponential suppression factor exp(-Delta/2h)^m, and we calculate all terms in this series, matching one-loop algebraic curve results from our previous paper arXiv:1006.2174. Starting with the second term, the structure of these terms is different to those in AdS_5 x S^5 thanks to the appearance of heavy modes in the loop, which can here be interpreted as two-particle bound states in the mirror theory. By contrast, physical bound states can represent dyonic giant magnons, and we also calculate F-terms for these solutions. Lüscher mu-terms, suppressed by exp(-Delta/E), instead give at leading order the classical finite-size correction. For an elementary dyonic giant magnon, we recover the correction given by arXiv:0903.3365. We then extend this to calculate the next term in 1/h, giving a one-loop prediction. Finally we also calculate F-terms for the various composite giant magnons, RP^3 and `big', again finding agreement to all orders.

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arXiv2011

The Near-Flat-Space and BMN Limits for Strings in AdS4 x CP3 at One Loop

This paper studies type IIA string theory in AdS4 x CP3 in both the BMN limit and the Maldacena-Swanson or near-flat-space limit. We derive the simpler Lagrangian for the latter limit by taking a large worldsheet boost of the BMN theory. We then calculate one-loop corrections to the correlators of the various fields using both theories. In all cases the near-flat-space results agree with a limit of the BMN results, providing evidence for the quantum consistency of this truncation. The corrections can also be compared to an expansion of the exact dispersion relation, known from integrability apart from one interpolating function h(lambda). Here we see agreement with the results of McLoughlin, Roiban & Tseytlin, and we observe that it does not appear to be possible to fully implement the cutoff suggested by Gromov & Mikhaylov, although for some terms we can do so. In both the near-flat-space and BMN calculations there are some extra terms in the mass shifts which break supersymmetry. These terms are extremely sensitive to the cutoff used, and can perhaps be seen as a consequence of using dimensional regularisation.

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arXiv2010

Quantum Strings and the AdS4/CFT3 Interpolating Function

The existence of a nontrivial interpolating function h(λ) is one of the novel features of the new AdS4/CFT3 correspondence involving ABJM theory. At strong coupling, most of the investigation of semiclassical effects so far has been for strings in the AdS4 sector. Several cutoff prescriptions have been proposed, leading to different predictions for the constant term in the expansion h(λ)=\sqrt{λ/2} + c + ... . We calculate quantum corrections for giant magnons, using the algebraic curve, and show by comparing to the dispersion relation that the same prescriptions lead to the same values of c in this CP3 sector. We then turn to finite-J effects, where a comparison with the Luescher F-term correction shows a mismatch for one of the three sum prescriptions. We also compute some dyonic and higher F-terms for future comparisons.

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arXiv2009

Dyonic Giant Magnons in CP^3: Strings and Curves at Finite J

This paper studies giant magnons in AdS_4 x CP^3 using both the string sigma-model and the algebraic curve. We complete the dictionary of solutions by finding the dyonic generalisation of the CP^1 string solution, which matches the `small' giant magnon in the algebraic curve, and by pointing out that the solution recently constructed by the dressing method is the `big' giant magnon. We then use the curve to compute finite-J corrections to all cases, which for the non-dyonic cases always match the AFZ result. For the dyonic RP^3 magnon we recover the S^5 answer, but for the `small' and `big' giant magnons we obtain new corrections.

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arXiv2008

Giant Magnons in AdS4 x CP3: Embeddings, Charges and a Hamiltonian

This paper studies giant magnons in CP3, which in all known cases are old solutions from S5 placed into two- and three-dimensional subspaces of CP3, namely CP1, RP2 and RP3. We clarify some points about these subspaces, and other potentially interesting three- and four-dimensional subspaces. After confirming that E-(J1-J4)/2 is a Hamiltonian for small fluctuations of the relevant 'vacuum' point particle solution, we use it to calculate the dispersion relation of each of the inequivalent giant magnons. We comment on the embedding of finite-J solutions, and use these to compare string solutions to giant magnons in the algebraic curve.

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arXiv2008

Vibrating giant spikes and the large-winding sector

The single spike is a rigidly rotating classical string configuration closely related to the giant magnon. We calculate bosonic and fermionic modes of this solution, from which we see that it is not supersymmetric. It can be viewed as an excitation above a hoop of string wound around the equator, in the same sense that the magnon is an excitation above an orbiting point particle. We find the operator which plays the role of the Hamiltonian for this sector, which compared to the magnon's E-J has the angular momentum replaced by a winding charge. The single spike solution is unstable, and we use the modes to attempt a semi-classical computation of its lifetime.

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arXiv2008

Six-Dimensional Yang Black Holes in Dilaton Gravity

We study the six-dimensional dilaton gravity Yang black holes of hep-th/0607193, which carry (1,-1) charge in SU(2)xSU(2) gauge group. We find what values of the asymptotic parameters (mass and scalar charge) lead to a regular horizon, and show that there are no regular solutions with an extremal horizon.

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