Narrow Results

Jacobi sigma models are two-dimensional topological nonlinear field theories which are associated with Jacobi structures. The latter can be considered as a generalization of Poisson structures. After reviewing the main properties and peculiarities of these models, we focus on the twisted version in which a Wess–Zumino term is included. This modification allows for the target space to be a twisted Jacobi manifold. We discuss in particular the model on the sphere $S^5$.

Fields exhibit a variety of topological properties, like different topological charges, when field space in the continuum is composed by more than one topological sector. Lattice treatments usually encounter difficulties describing those properties. In this work, we show that by augmenting the usual lattice fields to include extra variables describing local topological information (more precisely, regarding homotopy), the topology of the space of fields in the continuum is faithfully reproduced in the lattice. We apply this extended lattice formulation to some simple models with nontrivial topological charges, and we study their properties both analytically and via Monte Carlo simulations.

Four-dimensional Manin triples and Drinfeld doubles are classified and the corresponding two-dimensional Poisson–Lie T-dual sigma models on them are constructed. The simplest example of a Drinfeld double allowing decomposition into two nontrivially different Manin triples is presented.

In space–time dimensions larger than 2, whenever a global symmetry G is spontaneously broken to a subgroup H, and G and H are Lie groups, there are Nambu–Goldstone modes described by fields with values in G/H. In two-dimensional space–times as well, models where fields take values in G/H are of considerable interest even though in that case there is no spontaneous breaking of continuous symmetries. We consider such models when the world sheet is a two-sphere and describe their fuzzy analogs for G = SU(N+1), H = S(U(N-1) ⊗ U(1)) ≃ U(N) and . More generally our methods give fuzzy versions of continuum models on S² when the target spaces are Grassmannians and flag manifolds described by (N+1) × (N+1) projectors of rank ≤ (N+1)/2. These fuzzy models are finite-dimensional matrix models which nevertheless retain all the essential continuum topological features like solitonic sectors. They seem well suited for numerical work.

Non-singular global cosmic strings are found in a non-linear sigma model with a potential term for a self-gravitating complex scalar field. Stationary solutions with angular momentum and possibly linear momentum are obtained by assuming an oscillatory dependence of the scalar field on t, φ and z. This dependence has an effect similar to gauging the global U(1) symmetry of the model, which is actually a Kaluza-Klein reduction from four to three spacetime dimensions. The method of analysis can be regarded as an extension of the gravito-electromagnetism formalism beyond the weak field limit.

The solvable Lie algebra parametrization of the symmetric spaces is discussed. Based on the solvable Lie algebra gauge two equivalent formulations of the symmetric space sigma model are studied. Their correspondence is established by inspecting the normalization conditions and deriving the field transformation laws.

In this paper, the Weierstrass technique for harmonic maps S² → ℂP^N-1 is employed in order to obtain surfaces immersed in multidimensional Euclidean spaces. It is shown that if the ℂP^N-1 model equations are defined on the sphere S² and the associated action functional of this model is finite, then the generalized Weierstrass formula for immersion describes conformally parametrized surfaces in the su(N) algebra. In particular, for any holomorphic or antiholomorphic solution of this model the associated surface can be expressed in terms of an orthogonal projector of rank (N - 1). The implementation of this method is presented for two-dimensional conformally parametrized surfaces immersed in the su(3) algebra. The usefulness of the proposed approach is illustrated with examples, including the dilation-invariant meron-type solutions and the Veronese solutions for the ℂP² model. Depending on the location of the critical points (zeros and poles) of the first fundamental form associated with the meron solution, it is shown that the associated surfaces are semiinfinite cylinders. It is also demonstrated that surfaces related to holomorphic and mixed Veronese solutions are immersed in ℝ⁸ and ℝ³, respectively.

We explicitly solve the classical equations of motion for strings in backgrounds obtained as non-Abelian T-duals of a homogeneous isotropic plane-parallel wave. To construct the dual backgrounds, semi-Abelian Drinfeld doubles are used which contain the isometry group of the homogeneous plane wave metric. The dual solutions are then found by the Poisson–Lie transformation of the explicit solution of the original homogeneous plane wave background. Investigating their Killing vectors, we have found that the dual backgrounds can be transformed to the form of more general plane-parallel waves.

Basis tensor gauge theory (BTGT) is a vierbein analog reformulation of ordinary gauge theories in which the vierbein field describes the Wilson line. After a brief review of the BTGT, we clarify the Lorentz group representation properties associated with the variables used for its quantization. In particular, we show that starting from an SO(1,3) representation satisfying the Lorentz-invariant U(1,3) matrix constraints, BTGT introduces a Lorentz frame choice to pick the Abelian group manifold generated by the Cartan subalgebra of U(1,3) for the convenience of quantization even though the theory is frame independent. This freedom to choose a frame can be viewed as an additional symmetry of BTGT that was not emphasized before. We then show how an $S_4$ permutation symmetry and a parity symmetry of frame fields natural in BTGT can be used to construct renormalizable gauge theories that introduce frame-dependent fields but remain frame independent perturbatively without any explicit reference to the usual gauge field.

We consider target space duality transformations for heterotic sigma models and strings away from renormalization group fixed points. By imposing certain consistency requirements between the T-duality symmetry and renormalization group flows, the one-loop gauge beta function is uniquely determined, without any diagram calculations. Classical T-duality symmetry is a valid quantum symmetry of the heterotic sigma model, severely constraining its renormalization flows at this one-loop order. The issue of heterotic anomalies and their cancellation is addressed from this duality constraining viewpoint.

We consider the two-dimensional O(3) non-linear sigma model with topological term using a lattice regularization introduced by Shankar and Read [Nucl. Phys. B336, 457 (1990)], that is suitable for studying the strong coupling regime. When this lattice model is quantized, the coefficient θ of the topological term is quantized as θ=2πs, with s integer or half-integer. We study in detail the relationship between the low energy behaviour of this theory and the one-dimensional spin-s Heisenberg model. We generalize the analysis to sigma models with other symmetries.

In this paper, we explain how to derive the AdS₅×S⁵ supercoset sigma model in the Green-Schwarz formalism. The derivation is a generalization of the procedure for the PCM case developed by Delduc et al [arXiv:1909.13824]. This paper is based on the original paper [arXiv:2005.04950].

An interpretation of the gauge anomaly of the two-dimensional multi-phase σ-model is presented in terms of an obstruction to the existence of a topological defect network implementing a local trivialisation of the gauged σ-model.