Holography for confining gauge theories

This thesis explores di!erent applications of holography, the duality map between quantum field theories and quantum theories of gravity (string theories) in at least one higher dimension, to non-conformal and confining gauge theories. The first part investigates the thermal properties of strings in supergravity back- grounds dual to confining gauge theories, with particular regard to the Hagedorn phenomenon. In particular, general results on the Hagedorn temperature of planar, strongly coupled confining gauge theories holographically dual to type II superstring models on curved backgrounds with Ramond-Ramond and Kalb-Ramond fluxes and non- trivial dilaton are provided. For exact backgrounds, the Hagedorn temperature is determined up to next-to-next-to-next-to-leading order (NNNLO) in an expansion in the string length; in all the other cases, the results are reliably trusted up to NNLO. To reach these goals, di!erent complementary strategies are exploited. On the one hand, a worldsheet analysis, based on both an extrapolation to the Hagedorn regime of string semiclassical quantization and a “non-standard” semiclassical quan- tization approach, is presented. On the other hand, an e!ective method is pursued by perturbatively solving the equations of motion for the so-called thermal scalar field corresponding to the lightest mode of the winding string, which in flat space becomes tachyonic above the Hagedorn temperature. The interplay between these di!erent approaches is surely convenient, and yields both predictions for large N , strongly coupled gauge theories and precision tests of holography. The second part investigates a series of solutions of type IIB supergravity obtained from TsT transformations (a combination of T-dualities and coordinate shift) of seed backgrounds holographically dual to supersymmetry-preserving deformations of the N = 4 four-dimensional Super-Yang-Mills theory and of the Klebanov-Witten superconformal quiver gauge theory. The deformation provides novel non-trivial supergravity solutions dual to supersymmetric confining gauge theories in various dimensions. Focusing on disentangling the contributions of confinement, marginal deformations, and their interplay, key properties of the deformed theories, various observables, including Wilson loops, ’t Hooft loops, entanglement entropy, and central charge flow, are holographically analyzed. Additionally, a detailed study of how specific observables are a!ected by the dynamics of the Kaluza–Klein modes generated through circle compactification is presented. The results provide new insights into the non-perturbative dynamics of large N , strongly coupled field theories and highlight the predictive power of gauge/gravity duality beyond conformal and supersymmetric setups