Euler's disk is a toy described at http://www. eulersdisk. com. Aspects of its motion are mo... more Euler's disk is a toy described at http://www. eulersdisk. com. Aspects of its motion are modelled as an ideal disk rolling on a horizontal plane. In the final stages of Euler disk motions, the disk is nearly flat to the plane. Asymptotic approximations to the frequency of ...
We propose a Goldstino model formulated in terms of a constrained complex linear superfield. Its ... more We propose a Goldstino model formulated in terms of a constrained complex linear superfield. Its comparison to other Goldstino models is given. Couplings to supersymmetric matter and supergravity are briefly described.
Starting from the Akulov-Volkov (AV) action, we compute a finite-dimensional Lie group G of all f... more Starting from the Akulov-Volkov (AV) action, we compute a finite-dimensional Lie group G of all field transformations of the form λ → λ′ = λ + O(λ^3) which preserve the functional structure of low-energy Goldstino-like actions. Associated with G is its twelve-parameter subgroup H of trivial symmetries of the AV action. The coset space G/H is naturally identified with the space of all Goldstino models. We then apply our construction to study the properties of five different Goldstino actions available in the literature. Making use of the most general field redefinition derived, we find explicit maps between all five cases. In each case there is a twelve-parameter freedom in these maps due to trivial symmetries inherent in the Goldstino actions. Finally, by using the pushforward of the AV supersymmetry, we find the off-shell nonlinear supersymmetry transformations of the other five actions and compare to those normally associated with these actions.
Euler’s disk is a toy described at www.eulersdisk.com. Aspects
of its motion are modelled as an i... more Euler’s disk is a toy described at www.eulersdisk.com. Aspects of its motion are modelled as an ideal disk rolling on a horizontal plane. In the final stages of Euler disk motions, the disk is nearly flat to the plane. Asymptotic approximations to the frequency of finite amplitude oscillations on steady (non-dissipative) rolling motions of the Euler disk are described. There are two different approximations which are appropriate in different limits. When the parameters are such that both apply, the formulae for the frequency agree and is that given in §1.2: this appears to be new and simple. The material has been used in teaching. The teaching, and related, materials are available via the URL given at reference [4].
The full one-loop supersymmetric effective potential for the Wess-Zumino model is calculated usin... more The full one-loop supersymmetric effective potential for the Wess-Zumino model is calculated using superfield techniques. This includes the Kähler potential and the auxiliary field potential, of which the former was originally computed in 1993 while the latter is derived for the first time. In the purely bosonic sector our results match those of older component field calculations.
This thesis examines low-energy effective actions of supersymmetric quantum field theories. These... more This thesis examines low-energy effective actions of supersymmetric quantum field theories. These actions contain information about the low-energy field content and dynamics of quantum field theories and are essential for understanding their phenomenological and theoretical properties.
for N = 2 supersymmetric QED, due to a lesser amount of supersymmetry. Similarly to Ritus' analys... more for N = 2 supersymmetric QED, due to a lesser amount of supersymmetry. Similarly to Ritus' analysis for spinor and scalar QED, the two-loop renormalisation is carried out using proper-time cut-off regularisation. A closed-form expression is obtained for the holomorphic sector of the two-loop effective action, which is singled out by imposing a relaxed super self-duality condition.
In N=2 superconformal field theories the Kahler potential is known to be tree level exact. The be... more In N=2 superconformal field theories the Kahler potential is known to be tree level exact. The beta-deformation of N=4 SU(N) SYM reduces the amount of supersymmetry to N=1, allowing for non-trivial, superconformal loop corrections to the Kahler potential. We analyse the two-loop corrections on the Coulomb branch for a complex deformation. For an arbitrary chiral field in the Cartan subalgebra we reduce the problem of computing the two-loop Kahler potential to that of diagonalising the mass matrix, we then present the result in a manifestly superconformal form. The mass matrix diagonalisation is performed for the case of the chiral background that induces the breaking pattern SU(N) -> SU(N-2)*U(1)^2. Then, for the gauge group SU(3), the Kahler potential is explicitly computed to the two-loop order.
Euler's disk is a toy described at http://www. eulersdisk. com. Aspects of its motion are mo... more Euler's disk is a toy described at http://www. eulersdisk. com. Aspects of its motion are modelled as an ideal disk rolling on a horizontal plane. In the final stages of Euler disk motions, the disk is nearly flat to the plane. Asymptotic approximations to the frequency of ...
We propose a Goldstino model formulated in terms of a constrained complex linear superfield. Its ... more We propose a Goldstino model formulated in terms of a constrained complex linear superfield. Its comparison to other Goldstino models is given. Couplings to supersymmetric matter and supergravity are briefly described.
Starting from the Akulov-Volkov (AV) action, we compute a finite-dimensional Lie group G of all f... more Starting from the Akulov-Volkov (AV) action, we compute a finite-dimensional Lie group G of all field transformations of the form λ → λ′ = λ + O(λ^3) which preserve the functional structure of low-energy Goldstino-like actions. Associated with G is its twelve-parameter subgroup H of trivial symmetries of the AV action. The coset space G/H is naturally identified with the space of all Goldstino models. We then apply our construction to study the properties of five different Goldstino actions available in the literature. Making use of the most general field redefinition derived, we find explicit maps between all five cases. In each case there is a twelve-parameter freedom in these maps due to trivial symmetries inherent in the Goldstino actions. Finally, by using the pushforward of the AV supersymmetry, we find the off-shell nonlinear supersymmetry transformations of the other five actions and compare to those normally associated with these actions.
Euler’s disk is a toy described at www.eulersdisk.com. Aspects
of its motion are modelled as an i... more Euler’s disk is a toy described at www.eulersdisk.com. Aspects of its motion are modelled as an ideal disk rolling on a horizontal plane. In the final stages of Euler disk motions, the disk is nearly flat to the plane. Asymptotic approximations to the frequency of finite amplitude oscillations on steady (non-dissipative) rolling motions of the Euler disk are described. There are two different approximations which are appropriate in different limits. When the parameters are such that both apply, the formulae for the frequency agree and is that given in §1.2: this appears to be new and simple. The material has been used in teaching. The teaching, and related, materials are available via the URL given at reference [4].
The full one-loop supersymmetric effective potential for the Wess-Zumino model is calculated usin... more The full one-loop supersymmetric effective potential for the Wess-Zumino model is calculated using superfield techniques. This includes the Kähler potential and the auxiliary field potential, of which the former was originally computed in 1993 while the latter is derived for the first time. In the purely bosonic sector our results match those of older component field calculations.
This thesis examines low-energy effective actions of supersymmetric quantum field theories. These... more This thesis examines low-energy effective actions of supersymmetric quantum field theories. These actions contain information about the low-energy field content and dynamics of quantum field theories and are essential for understanding their phenomenological and theoretical properties.
for N = 2 supersymmetric QED, due to a lesser amount of supersymmetry. Similarly to Ritus' analys... more for N = 2 supersymmetric QED, due to a lesser amount of supersymmetry. Similarly to Ritus' analysis for spinor and scalar QED, the two-loop renormalisation is carried out using proper-time cut-off regularisation. A closed-form expression is obtained for the holomorphic sector of the two-loop effective action, which is singled out by imposing a relaxed super self-duality condition.
In N=2 superconformal field theories the Kahler potential is known to be tree level exact. The be... more In N=2 superconformal field theories the Kahler potential is known to be tree level exact. The beta-deformation of N=4 SU(N) SYM reduces the amount of supersymmetry to N=1, allowing for non-trivial, superconformal loop corrections to the Kahler potential. We analyse the two-loop corrections on the Coulomb branch for a complex deformation. For an arbitrary chiral field in the Cartan subalgebra we reduce the problem of computing the two-loop Kahler potential to that of diagonalising the mass matrix, we then present the result in a manifestly superconformal form. The mass matrix diagonalisation is performed for the case of the chiral background that induces the breaking pattern SU(N) -> SU(N-2)*U(1)^2. Then, for the gauge group SU(3), the Kahler potential is explicitly computed to the two-loop order.
Uploads
Papers by Simon Tyler
of its motion are modelled as an ideal disk rolling on a horizontal plane. In the final stages of Euler disk motions, the disk is nearly flat to the plane. Asymptotic approximations to the frequency of finite amplitude oscillations on steady (non-dissipative) rolling motions of the Euler disk are described. There are two different approximations which are appropriate in different limits. When the parameters are such that both apply, the formulae for the frequency agree and is that given in §1.2: this appears to be new and simple.
The material has been used in teaching. The teaching, and related, materials are available via the URL given at reference [4].
of its motion are modelled as an ideal disk rolling on a horizontal plane. In the final stages of Euler disk motions, the disk is nearly flat to the plane. Asymptotic approximations to the frequency of finite amplitude oscillations on steady (non-dissipative) rolling motions of the Euler disk are described. There are two different approximations which are appropriate in different limits. When the parameters are such that both apply, the formulae for the frequency agree and is that given in §1.2: this appears to be new and simple.
The material has been used in teaching. The teaching, and related, materials are available via the URL given at reference [4].