From conformal to confining field theories using holography

From conformal to confining field theories using holography

4 Mar 2024 | Ali Fatemiabhari and Carlos Nunez
This paper presents a new family of Type IIB supergravity backgrounds that are dual to five-dimensional conformal field theories (CFTs) compactified and deformed by vacuum expectation values (VEVs) of certain operators. These backgrounds generate a renormalization group (RG) flow into a smooth background dual to non-supersymmetric (non-SUSY) gapped field theories in four dimensions. The authors study various holographic observables, including a monotonic quantity associated with the number of degrees of freedom, Wilson loops that interpolate between conformal and confining behavior, entanglement entropy, and holographic complexity. They also calculate the spectrum of spin-two glueballs in the field theories. The supergravity background is constructed using a set of coordinates and functions that describe the geometry of the dual field theories. The background is smooth everywhere except at the position of localized D7 brane sources (flavor branes). The authors calculate Page charges, finding that the background consists of an array of D5-NS5 and D7 branes, which correspond to a balanced linear quiver in the dual field theory. The number of branes determines the structure of the quiver. The dual field theories are studied using holography, with a focus on the behavior of the field theories across different energy scales. The authors introduce a monotonic quantity, called the flow-central charge, which measures the number of degrees of freedom along the RG flow. This quantity is constant at both ends of the flow and is sensitive to the presence of a UV fixed point and an IR gapped QFT. The authors also study Wilson loops, which are used to probe the behavior of the dual field theories at low energies. They find that Wilson loops exhibit conformal behavior at small separations between quarks and transition to confining behavior at larger separations. The presence of localized sources (D7 branes) allows for screening, which is consistent with the presence of a non-SUSY gapped QFT in the IR. The authors calculate the holographic complexity for these backgrounds, finding that it is related to the free energy of the 5d SCFT and has contributions from the RG flow away from the fixed point. They also compute the masses of spin-two excitations in the four-dimensional Minkowski part of the space, finding that the spectrum consists of positive masses, indicating the stability of the non-SUSY QFT. The paper concludes with a discussion of the implications of these results for the understanding of non-SUSY field theories and their holographic duals. The authors also mention possible future directions for research, including further study of the holographic complexity and the behavior of the dual field theories in different limits.This paper presents a new family of Type IIB supergravity backgrounds that are dual to five-dimensional conformal field theories (CFTs) compactified and deformed by vacuum expectation values (VEVs) of certain operators. These backgrounds generate a renormalization group (RG) flow into a smooth background dual to non-supersymmetric (non-SUSY) gapped field theories in four dimensions. The authors study various holographic observables, including a monotonic quantity associated with the number of degrees of freedom, Wilson loops that interpolate between conformal and confining behavior, entanglement entropy, and holographic complexity. They also calculate the spectrum of spin-two glueballs in the field theories. The supergravity background is constructed using a set of coordinates and functions that describe the geometry of the dual field theories. The background is smooth everywhere except at the position of localized D7 brane sources (flavor branes). The authors calculate Page charges, finding that the background consists of an array of D5-NS5 and D7 branes, which correspond to a balanced linear quiver in the dual field theory. The number of branes determines the structure of the quiver. The dual field theories are studied using holography, with a focus on the behavior of the field theories across different energy scales. The authors introduce a monotonic quantity, called the flow-central charge, which measures the number of degrees of freedom along the RG flow. This quantity is constant at both ends of the flow and is sensitive to the presence of a UV fixed point and an IR gapped QFT. The authors also study Wilson loops, which are used to probe the behavior of the dual field theories at low energies. They find that Wilson loops exhibit conformal behavior at small separations between quarks and transition to confining behavior at larger separations. The presence of localized sources (D7 branes) allows for screening, which is consistent with the presence of a non-SUSY gapped QFT in the IR. The authors calculate the holographic complexity for these backgrounds, finding that it is related to the free energy of the 5d SCFT and has contributions from the RG flow away from the fixed point. They also compute the masses of spin-two excitations in the four-dimensional Minkowski part of the space, finding that the spectrum consists of positive masses, indicating the stability of the non-SUSY QFT. The paper concludes with a discussion of the implications of these results for the understanding of non-SUSY field theories and their holographic duals. The authors also mention possible future directions for research, including further study of the holographic complexity and the behavior of the dual field theories in different limits.
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[slides and audio] From conformal to confining field theories using holography