q-form global symmetries generalize ordinary symmetries to higher-dimensional charged objects, leading to new rules for amplitudes, gauging, breaking, and anomaly inflow in quantum field theories.
Geometric Langlands From Six Dimensions
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abstract
Geometric Langlands duality is usually formulated as a statement about Riemann surfaces, but it can be naturally understood as a consequence of electric-magnetic duality of four-dimensional gauge theory. This duality in turn is naturally understood as a consequence of the existence of a certain exotic supersymmetric conformal field theory in six dimensions. The same six-dimensional theory also gives a useful framework for understanding some recent mathematical results involving a counterpart of geometric Langlands duality for complex surfaces. (This article is based on a lecture at the Raoul Bott celebration, Montreal, June 2008.)
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A D5-D7 brane configuration in AdS5 x S5 provides an interpolating holographic dual for defect CFTs, with anomaly cancellation and a conjectured SYM solution.
The type-A Weyl anomaly coefficient b for holographic defect CFTs is negative in a finite parameter region at both weak and strong coupling, providing the first explicit example of an interacting unitary dCFT with b<0.
The spectrum E = R²(e^p + e^{-p}) + (e^x + e^{-x}) from local P¹ × P¹ is identified with the almost Mathieu operator, yielding three spectral phases separated by transitions at R² = 1 and R² = e^β.
Lecture notes that systematically introduce higher-form symmetries, SymTFTs, higher-group symmetries, and related concepts in QFT using gauge theory examples.
citing papers explorer
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Generalized Global Symmetries
q-form global symmetries generalize ordinary symmetries to higher-dimensional charged objects, leading to new rules for amplitudes, gauging, breaking, and anomaly inflow in quantum field theories.
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Holographic interpolations of defect CFTs
A D5-D7 brane configuration in AdS5 x S5 provides an interpolating holographic dual for defect CFTs, with anomaly cancellation and a conjectured SYM solution.
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Weyl Anomaly Coefficients of Holographic Defect CFTs at Weak and Strong Coupling
The type-A Weyl anomaly coefficient b for holographic defect CFTs is negative in a finite parameter region at both weak and strong coupling, providing the first explicit example of an interacting unitary dCFT with b<0.
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Geometric Engineering and Almost Mathieu Operator
The spectrum E = R²(e^p + e^{-p}) + (e^x + e^{-x}) from local P¹ × P¹ is identified with the almost Mathieu operator, yielding three spectral phases separated by transitions at R² = 1 and R² = e^β.
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Lectures on Generalized Symmetries
Lecture notes that systematically introduce higher-form symmetries, SymTFTs, higher-group symmetries, and related concepts in QFT using gauge theory examples.