| 1. |
- Bundzik, Daniel
(author)
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Aspects of the Duality between Supersymmetric Yang-Mills Theory and String Theory
- 2007
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Doctoral thesis (other academic/artistic)abstract
- This thesis deals with three topics related to the Ads/CFT correspondence. In Paper I, solutions describing the geometry of fractional D1-branes of Type IIB string theory are presented. The running coupling constant is computed on the gauge theory side. Paper II uses the idea that the anomalous dimension of a gauge theory operator can be interpreted as an eigenvalue of a spin chain Hamiltonian. The general Leigh-Strassler deformation is rewritten in terms of a spin-one spin chain and the integrability properties of the corresponding Hamiltonian are studied. In paper III a non-commutative multiplication law, a star product, is defined. From this star product the general Leigh-Strassler deformation is obtained, and it is shown that the deformation only results in prefactors to the amplitudes of the undeformed theory.
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| 2. |
- Bundzik, Daniel
(author)
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Star product and the general Leigh-Strassler deformation
- 2007
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In: Journal of High Energy Physics (JHEP). - : SISSA. - 1126-6708 .- 1029-8479. ; :04
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Journal article (peer-reviewed)abstract
- We extend the definition of the star product introduced by Lunin and Maldacena to study marginal deformations of = 4 SYM. The essential difference from the latter is that instead of considering U(1) × U(1) non-R-symmetry, with charges in a corresponding diagonal matrix, we consider two 3-symmetries followed by an SU(3) transformation, with resulting off-diagonal elements. From this procedure we obtain a more general Leigh–Strassler deformation, including cubic terms with the same index, for specific values of the coupling constants. We argue that the conformal property of = 4 SYM is preserved, in both β- (one-parameter) and γi-deformed (three-parameters) theories, since the deformation for each amplitude can be extracted in a prefactor. We also conclude that the obtained amplitudes should follow the iterative structure of MHV amplitudes found by Bern, Dixon and Smirnov.
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| 3. |
- Bundzik, Daniel, et al.
(author)
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The general Leigh-Strassler deformation and integrability
- 2006
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In: Journal of High Energy Physics. - : Springer Science and Business Media LLC. - 1029-8479 .- 1126-6708. ; :1
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Journal article (peer-reviewed)abstract
- The success of the identification of the planar dilatation operator of N = 4 SYM with an integrable spin chain Hamiltonian has raised the question if this also is valid for a deformed theory. Several deformations of SYM have recently been under investigation in this context. In this work we consider the general Leigh-Strassler deformation. For the generic case the S-matrix techniques cannot be used to prove integrability. Instead we use R-matrix techniques to study integrability. Some new integrable points in the parameter space are found.
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| 4. |
- Bundzik, Daniel, et al.
(author)
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The geometry of fractional D1-branes
- 2004
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In: Classical and Quantum Gravity. - : IOP Publishing. - 1361-6382 .- 0264-9381. ; 21:16, s. 3985-3993
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Journal article (peer-reviewed)abstract
- We find explicit solutions of type IIB string theory on R-4/Z(2) corresponding to the classical geometry of fractional D1-branes. From the supergravity solution obtained, we capture perturbative information about the running of the coupling constant and the metric on the moduli space of N = 4, D = 2 super Yang-Mills.
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