55th North British Mathematical Physics Seminar

The 55th meeting of the North British Mathematical Physics Seminar will be held on Wednesday 27 March 2019 in Edinburgh at ICMS which is located at at The Bayes Centre, 47 Potterrow, Edinburgh EH8 9BT, seminar room 5.02. For all general information about the North British Mathematical Physics Seminar, including instruction for claiming travel expenses follow this link

Programme

Abstract: Michael Atiyah exerted a profound influence on mathematical physics over the past fifty years, which took three distinct forms: an indirect impact through the applications of his work in geometry and topology, a direct impact through his own research in theoretical and mathematical physics, often in collaboration with physicists, and finally a pedagogical impact which helped geometers and physicists to find a common language. In this talk I will illustrate Michael's influence on mathematical physics and physicists with examples - and pictures.

Abstract:During the last few years there has been a transformation in our understanding of symmetries and anomalies. The fundamental ideas ultimately originate from condensed matter physics, and more specifically from the classification of topological phases of matter. I will review the basics of the modern viewpoint, and explain a number of results that follow from applying this philosophy to particle physics. Briefly, we will find that the Standard Model is anomaly-free on arbitrary spacetime topologies (oriented and unoriented), a natural Z_4 refinement of (-1)^F (with F the fermion number) is anomaly free only if the number of fermions in the SM is a multiple of 16, and proton triality being anomaly-free implies that the number of generations is a multiple of 3.

Abstract: M-theory in AdS7xS4 is dual to a six-dimensional superconformal field theory with (2,0) supersymmetry and it reduces to 11d supergravity at low energies. Higher-derivative corrections to tree-level supergravity are encoded in the anomalous dimensions of double-trace operators occurring in the conformal partial wave expansion of four-point stress tensor correlators in the 6d (2,0) theory. I will describe recursion relations for these anomalous dimensions which are derived using conformal bootstrap methods.

Abstract: The amplituhedron provides a beautiful description of perturbative superamplitude integrands in N=4 SYM in terms of purely geometric objects, generalisations of polytopes. On the other hand the Wilson loop in supertwistor space also gives an explicit description of these superamplitudes as a sum of planar Feynman diagrams. Each Feynman diagram can be naturally associated with a geometrical object in the same space as the amplituhedron (although not uniquely). This suggests that these geometric images of the Feynman diagrams give a tessellation of the amplituhedron. I will begin by introducing the amplituhedron and the twistor wilson loop, and then go on to show that beyond NMHV this turns out not to be the case.

Abstract:The Truncated Conformal Space Approach (TCSA) is a numerical method of calculating the spectrum of finite dimensional Hamiltonian operators. It is based on the truncation of the infinite dimensional Hilbert space to some finite subspace on which the Hamiltonian can then be diagonalised numerically. I apply the method here in the context of boundary perturbations of conformal fixed points, investigating the resulting RG flows. In particular, I will focus on the approach to the IR fixed point in the Ising and Tricritical Ising models, investigating the dominant operators which drive the approach. Time permitting, I will discuss a known feature of the TCSA spectrum: flows beyond the fixed point.

Abstract:In this talk I will discuss the expansion of general relativity in inverse powers of the speed of light. This expansion can be truncated at any desired order and, when truncated at the next-to-leading order, it can be used to derive an action principle for a diffeomorphism invariant description of non-relativistic gravity. This describes Newtonian gravity as well as strong gravity extensions thereof (e.g. due to time dilation effects). I will show how to couple such a theory to matter (point particles, scalar fields and fluids) and use this to show that the Tolman-Oppenheimer-Volkov star solution and the Friedmann equations can both be viewed as solutions to the equations of motion of matter coupled non-relativistic gravity. By looking at geodesics in a spherically symmetric background one can show that the phenomenon of perihelion precession is also described by this theory. Time permitting I will end with some comments about string and holographic extensions of these results.

Practical Information

ICMS is a 20-25 minute walk from Waverley train station. Here is a link to ICMS web page here .

Limited funds are available to help with travel expenses of participants with no other source of funding. We hope that this will encourage postgraduate students and postdocs to attend the meeting. Please email Benoit Vicedo in advance if you would like to apply for support.

Postscript: The meeting took place successfully. Click here to view a list of people who took part.