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Register a new userNon-Lorentzian M5-brane Theories from Holography
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M-theory on $AdS_7 times S^4$ admits a description where the $AdS_7$ factor is constructed as a timelike Hopf fibration over a non-compact three dimensional complex projective space $tilde{mathbb{CP}}^3$. We consider the worldvolume theory for M5-branes at a fixed $tilde{mathbb{CP}}^3$ radius which, after reduction along the timelike fibre, is given by an $Omega$-deformed Yang-Mills theory with eight supercharges. Taking the radius to infinity then induces a classical RG flow. We construct the fixed point action which has an enhanced 24 supercharges and which can be understood as the $(2,0)$ theory of M5-branes on flat space reduced along a compact null Killing direction.
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We study loop corrections to scattering amplitudes in the world-volume theory of a probe D3-brane, which is described by the supersymmetric Dirac-Born-Infeld theory. We show that the D3-brane loop superamplitudes can be obtained from the tree-level superamplitudes in the world-volume theory of a probe M5-brane (or D5-brane). The M5-brane theory describes self-interactions of an abelian tensor supermultiplet with $(2,0)$ supersymmetry, and the tree-level superamplitudes are given by a twistor formula. We apply the construction to the maximally-helicity-violating (MHV) amplitudes in the D3-brane theory at one-loop order, which are purely rational terms (except for the four-point amplitude). The results are further confirmed by generalised unitarity methods. Through a supersymmetry reduction on the M5-brane tree-level superamplitudes, we also construct one-loop corrections to the non-supersymmetric D3-brane amplitudes, which agree with the known results in the literature.
We construct families of supersymmetric AdS$_3times Y_7$ and AdS$_3times Y_8$ solutions to type IIB string theory and M-theory, respectively. Here $Y_7$ is an $S^5$ fibration over $Sigma$, while $Y_8$ is an $S^4$ fibration over $Sigma_gtimes Sigma$, where $Sigma_g$ is a Riemann surface of genus $g>1$ and $Sigma$ is a two-dimensional orbifold known as a spindle. We interpret the solutions as near-horizon limits of $N$ D3-branes wrapped on $Sigma$ and $N$ M5-branes wrapped on $Sigma_gtimes Sigma$, respectively. These are holographically dual to $d=2$, $(0,2)$ SCFTs, and we show that the central charge and superconformal R-symmetry of the gravity solutions agree with dual field theory calculations.
In this thesis we investigate some aspects of quantum field theories from a holographic perspective. In the first chapters we examine in detail a one-paremeter family of three-dimensional gauge theories by means of their type IIA gravity duals. We analyse features such as their confinement nature, spectrum, entanglement properties or thermal phase transitions. This family interpolates between quasi-conformal and quasi-confining physics. In the last two chapters, we use bottom-up models to study complex conformal field theories and transport properties of dense QCD respectively.
We highlight what seems to be a remaining subtlety in the argument for the cancellation of the total anomaly associated with the M5-brane in M-theory. Then we prove that this subtlety is resolved under the hypothesis that the C-field flux is charge-quantized in the generalized cohomology theory called J-twisted Cohomotopy.
We revisit the idea that the quantum dynamics of open strings ending on $N$ D3-branes in the large $N$ limit can be described at large `t Hooft coupling by classical closed string theory in the background created by the D3-branes in asymptotically flat spacetime. We study the resulting thermodynamics and compute the Hagedorn temperature and other properties of the D3-brane worldvolume theory in this regime. We also consider the theory in which the D3-branes are replaced by negative branes and show that its thermodynamics is well behaved. We comment on the idea that this theory can be thought of as an irrelevant deformation of $mathcal{N}=4$ SYM, and on its relation to $Tbar T$ deformed $CFT_2$.
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