The Coon amplitude is a deformation of the Veneziano amplitude with logarithmic Regge trajectories and an accumulation point in the spectrum, which interpolates between string theory and field theory. With string theory, it is the only other solution to duality constraints explicitly known and it constitutes an important data point in the modern S-matrix bootstrap. Yet, its basics properties are essentially unknown. In this paper we fill this gap and derive the conditions of positivity and the low energy expansion of the amplitude. On the positivity side, we discover that the amplitude switches from a regime where it is positive in all dimensions to a regime with critical dimensions, that connects to the known d = 26, 10 when the deformation is removed. En passant, we find that the Veneziano amplitudes can be extended to massive scalars of masses up to m^2 = 1/3, where it has critical dimension 6.3. On the low-energy side, we compute the first few couplings of the theory in terms of q-deformed analogues of the standard Riemann zeta values of the string expansion. We locate their location in the EFT-hedron, and find agreement with a recent conjecture that theories with accumulation points populate this space. We also discuss their relation to low spin dominance.

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I will talk about a new type of critical quantum liquids, dubbed Stiefel liquids, that can emerge in quantum magnets. Our theory is based on 2+1 dimensional nonlinear sigma models on target space SO(N)/SO(4), supplemented with Wess-Zumino-Witten terms. We argue that the Stiefel liquids form a class of 3d CFTs with extraordinary properties, such as large emergent symmetries, a cascade structure, and nontrivial quantum anomalies. We show that the well known deconfined quantum critical point and U(1) Dirac spin liquid (i.e. Nf=4 QED3) are unified as two special examples of Stiefel liquids, with N=5 and N=6, respectively. Furthermore, we conjecture that Stiefel liquids with N>6 are non-Lagrangian, in the sense that under renormalization group they flow to infrared (conformally invariant) fixed points that cannot be described by any renormalizable continuum Lagrangian. I will also discuss a physical way to realize Stiefel liquids (both the Dirac spin liquid and N=7 non-Lagrangian Stiefel liquid) in quantum spin systems, for example, on triangular or kagome lattice, through the intertwinement of symmetry breaking orders.

Participer à la réunion Zoom
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Séminaire « Equations différentielles »

In 1896 Frobenius and Fricke published two seemingly unrelated papers: Frobenius started to develop his theory of k-characters for finite groups motivated by Dedekind’s question about factorisation of the group determinant, while Fricke followed Klein’s approach to the uniformization theorem. I will explain that in fact these two works can be naturally linked and both are related to remarkable Markov’s paper of 1880 on arithmetic of binary quadratic forms. The talk is based on a joint work with V.M. Buchstaber.

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Séminaire « Equations différentielles »

Some standard differential equations with irregular singularities, like Airy or Kloosterman and their symmetric products, behave in a way similar to Gauss-Manin differential equations , and their de Rham cohomology underlie a mixed Hodge structure, possibly with finite monodromy, enabling the use of tame arithmetic methods to handle the associated exponential sums. The talk will mainly focus on the Airy case, after a joint work with Jeng-Daw Yu.

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Séminaire « Equations différentielles »

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Quantum representations form a family of representations of modular groups of surfaces with values in projective pseudo-unitary groups PU(p,q), sending Dehn twists to finite-order elements. Toledo invariants of these representations, and more general characteristic classes, extend to cohomology classes defined on the Deligne-Mumford compactification of moduli spaces, defining cohomological field theories (CohFT). We will give explicit formulae for the Toledo part of the latter in some cases, including Fibonacci quantum representations. This allows to construct/recover complex hyperbolic structures on some moduli spaces. Work in progress with Julien Marché.

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Positivity is meant as a generalisation of the cyclic order on the circle. Associated to that is the notion of monotone maps from a cyclically ordered set in the circle.

Generalisations of the idea of positivity appeared to be crucial in understanding some connected components of the space of representations of a surface group in a Lie group G, although the common phenomenon was not figured out until recently.

In this talk, based on a preprint with Olivier Guichard and Anna Wienhard, I will start by examples generalizing this notion of cyclic order on the circle: convex curves or configurations in the plane, time like curve in Minkowski space. Then I will move to the general geometry of parabolic spaces and explain why the notion of positivity relates to special configurations of pairwise transverse triples and quadruples of points. This notion of positivity, which abides simple combinatorial properties, allows to define positive — or monotone — curves, then positive representations of surface groups.

I will then sketch the proof of our main result: positive representations are Anosov and fill up connected components of the space of representations.

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Séminaire Laurent Schwartz — EDP et applications

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Séminaire Laurent Schwartz — EDP et applications

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IHES Covid-19 regulations:

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Séminaire « Equations différentielles »

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IHES Covid-19 regulations:

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Séminaire « Equations différentielles »

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IHES Covid-19 regulations:

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Séminaire Laurent Schwartz — EDP et applications

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IHES Covid-19 regulations:

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