The worldsheet dual of free super Yang-Mills in 4D

The worldsheet string theory dual to free 4d $$ \mathcal{N} $$ N = 4 super Yang-Mills theory was recently proposed in [1]. It is described by a free field sigma model on the twistor space of AdS5 × S5, and is a direct generalisation of the corresponding model for tensionless string theory on AdS3 × S3. As in the case of AdS3, the worldsheet theory contains spectrally flowed representations. We proposed in [1] that in each such sector only a finite set of generalised zero modes (‘wedge modes’) are physical. Here we show that after imposing the appropriate residual gauge conditions, this worldsheet description reproduces precisely the spectrum of the planar gauge theory. Specifically, the states in the sector with w units of spectral flow match with single trace operators built out of w super Yang-Mills fields (‘letters’). The resulting physical picture is a covariant version of the BMN light-cone string, now with a finite number of twistorial string bit constituents of an essentially topological worldsheet.

On A. D. Sakharov’s Hypothesis of Cosmological Transitions with Changes in the Signature of the Metric

The paper discusses possible consequences of A. D. Sakharov’s hypothesis of cosmological transitions with changes in the signature of the metric, based on the path integral approach. This hypothesis raises a number of mathematical and philosophical questions. Mathematical questions concern the definition of the path integral to include integration over spacetime regions with different signatures of the metric. One possible way to describe the changes in the signature is to admit time and space coordinates to be purely imaginary. It may look like a generalization of what we have in the case of pseudo-Riemannian manifolds with a non-trivial topology. The signature in these regions can be fixed by special gauge conditions on components of the metric tensor. The problem is what boundary conditions should be imposed on the boundaries of these regions and how they should be taken into account in the definition of the path integral. The philosophical question is what distinguishes the time coordinate among other coordinates but the sign of the corresponding principal value of the metric tensor. In particular, there is an attempt in speculating how the existence of the regions with different signature can affect the evolution of the Universe.

Soft-collinear effective theory: BRST formulation

We provide a BRST formalism for the soft-collinear effective theory describing interactions of soft and collinear degrees of freedom in the presence of a hard interaction. In particular, we develop a BRST symmetry transformation for SCET theory. We further generalize the BRST formulation by making the transformation parameter field dependent. This establishes a mapping between several SCET actions consistently when defined in different gauge conditions. In fact, a definite structure of gauge-fixed actions corresponding to any particular gauge condition can be generated for SCET theory using our formulation.

Cartan's Approach to Second Order Ordinary Differential Equations

In his work on projective connections, Cartan discusses his theory of second order differential euqtions . It is the aim here to look at how a normal projective connection can be constructed and how it relates to the geometry of a single second order differential equation. The calculations are presented in some detail in order to highlight the usage of gauge conditions.

From complex holomorphic systems to real systems

Symmetries in modern physics are a fundamental subject of high relevance that allows appreciating more deeply the physical structure of a theory. In this paper, we analyze a gauge symmetry that appears in complex holomorphic systems. We show that a complex system can be reduced to different real systems, using different gauge conditions, and the gauge transformations connect several real systems in the complex space. We prove that the space of solutions of one system is related using a gauge transformation to another one. Gauge transformations are, in some cases, canonical transformations. However, in other cases, these are more general transformations that change the symplectic structure, but there is still a map between systems. We establish a construction to extend the analysis to the quantum case using path integrals through the Batalin–Fradkin–Vilkovisky theorem and within the canonical formalism, where we show explicitly that solutions of the Schrödinger equation are gauge-related.

Electromagnetic Wave Equations of Dyon in Arbitrary Media

Dyon is a hypothetical particle in high energy physics that carries simultaneously both electric and magnetic charge. A dyon with zero electric charge is referred to a magnetic monopole. The paper, reports a simple reformulation of Maxwell equations for dyon in arbitrary media. The Lorentz, Coulomb gauge conditions and the wave equations of dyon in arbitrary media are derived in a simple and compact manner.

Faddeev–Jackiw quantization of Christ–Lee model

We analyze the constraints of Christ–Lee model by means of modified Faddeev–Jackiw formalism in Cartesian as well as polar coordinates. Further, we accomplish quantization à la Faddeev–Jackiw by choosing appropriate gauge conditions in both the coordinate systems. Finally, we establish gauge symmetries of Christ–Lee model with the help of zero-modes of the symplectic matrix.