insight - Computational Complexity - # Holographic RG flows and Janus interfaces in F(4) gauged supergravity

Core Concepts

The author studies six-dimensional F(4) gauged supergravity coupled to four vector multiplets with a non-semisimple ISO(3)×U(1) gauge group, which arises from a consistent truncation of type IIB string theory. The gauged supergravity admits three critical points corresponding to supersymmetric AdS6, non-supersymmetric AdS6, and dS6 geometries. The author computes the scalar masses and finds that only the supersymmetric AdS6 vacuum is stable. By truncating to SO(3)×U(1) and SO(2)×U(1) invariant sectors, the author studies holographic RG flow solutions from the supersymmetric AdS6 critical point to various non-conformal phases of the dual five-dimensional N=2 SCFT. The author also derives supersymmetric Janus solutions describing conformal interfaces within the five-dimensional SCFT.

Abstract

The paper studies the F(4) gauged supergravity in six dimensions coupled to four vector multiplets with a non-semisimple ISO(3)×U(1) gauge group. This gauged supergravity arises from a consistent truncation of type IIB string theory on S2×Σ, where Σ is a Riemann surface.

The author first identifies the critical points of the scalar potential, which include a supersymmetric AdS6 vacuum, a non-supersymmetric AdS6 vacuum, and a dS6 vacuum. The scalar masses are computed, and it is found that only the supersymmetric AdS6 vacuum is stable.

The author then studies holographic RG flow solutions from the supersymmetric AdS6 critical point. By truncating to SO(3)×U(1) and SO(2)×U(1) invariant sectors, the author finds various RG flow solutions that describe the dual five-dimensional N=2 SCFT flowing to different non-conformal phases. The RG flows are driven by both relevant and irrelevant operators.

Additionally, the author derives supersymmetric Janus solutions that describe conformal interfaces within the five-dimensional SCFT. These Janus solutions interpolate between the AdS6 vacua at the two limits.

The results provide the first holographic studies of matter-coupled F(4) gauged supergravity with a non-semisimple gauge group, in contrast to the previous works that focused on compact gauge groups.

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arxiv.org

Stats

The scalar masses at the supersymmetric AdS6 vacuum are given in Table 1.
The scalar masses at the non-supersymmetric AdS6 vacuum are given in Table 2.
The scalar masses at the dS6 vacuum are given in Table 3.

Quotes

"We study six-dimensional F(4) gauged supergravity coupled to four vector multiplets with a non-semisimple ISO(3) × U(1) gauge group."
"We find that the gauged supergravity admit three SO(3) symmetric vacua given by N = (1, 1) supersymmetric AdS6, non-supersymmetric AdS6 and dS6 geometries."
"We compute all scalar masses at all of these critical points and find that only the supersymmetric AdS6 vacuum is stable."

Key Insights Distilled From

by Parinya Karn... at **arxiv.org** 10-01-2024

Deeper Inquiries

The presence of both relevant and irrelevant operators at the supersymmetric AdS6 critical point introduces a richer structure to the holographic duality compared to previous studies that only considered relevant operators. In the context of the AdS/CFT correspondence, relevant operators correspond to perturbations that can drive the system away from the conformal fixed point, leading to non-conformal phases of the dual N = 2 superconformal field theory (SCFT). The inclusion of irrelevant operators, which typically have dimensions greater than the critical dimension, suggests that the system can exhibit more complex behavior, including the possibility of additional phases or transitions that are not captured by relevant operators alone.
In particular, the scalar masses at the AdS6 vacuum indicate that the irrelevant operators can influence the stability and dynamics of the RG flows. While relevant operators can lead to a flow towards a non-conformal phase, the presence of irrelevant operators may introduce additional constraints or modify the flow's trajectory, potentially leading to new fixed points or singularities. This duality between the operator dimensions and the stability of the vacuum states highlights the intricate interplay between the geometry of the AdS space and the field theory dynamics, paving the way for further exploration of the implications of these operators in holographic models.

The unphysical singularities encountered in some RG flow solutions can potentially be resolved by uplifting the six-dimensional solutions to ten dimensions, particularly within the framework of type IIB string theory. In the context of the AdS/CFT correspondence, the six-dimensional gauged supergravity models studied here arise from consistent truncations of type IIB string theory on specific geometries, such as S2 × Σ, where Σ is a Riemann surface.
When uplifting to ten dimensions, one can utilize the full machinery of string theory, including the dynamics of additional fields and the geometry of the compactification. This process often reveals that what appears as a singularity in the lower-dimensional effective theory may correspond to a more regular structure in the higher-dimensional theory, such as a brane configuration or a resolved geometry. The uplifting procedure can also provide additional degrees of freedom that may smooth out the singularities, leading to physically acceptable solutions that correspond to well-defined configurations in the dual SCFT.
Moreover, the uplifting can help identify the nature of the singularities—whether they are artifacts of the truncation or genuine features of the underlying string theory. By analyzing the ten-dimensional solutions, one can ascertain whether the singularities can be interpreted as physical phenomena, such as the presence of D-branes or other topological defects, which would enrich the understanding of the duality and the associated field theory dynamics.

Yes, the physical singularities identified in this work can indeed be interpreted as brane configurations in the dual type IIB theory. In the context of the AdS/CFT correspondence, singularities in the gravitational description often correspond to specific physical phenomena in the dual field theory, such as the presence of defects, interfaces, or branes.
In particular, the Janus solutions and other configurations studied in the paper suggest that the singularities may represent the locations of D-branes or other types of branes in the ten-dimensional type IIB framework. These branes can support various field theory dynamics, including the breaking of supersymmetry or the introduction of new degrees of freedom that affect the behavior of the dual SCFT.
The interpretation of singularities as brane configurations is supported by the fact that branes can lead to localized sources of energy and can modify the geometry of the surrounding spacetime. This modification can manifest as singularities in the lower-dimensional effective theory, which, when uplifted, reveal the underlying brane structure. Thus, the physical singularities observed in the RG flow solutions not only provide insights into the dynamics of the dual SCFT but also enrich the understanding of the geometric and topological aspects of the string theory landscape.

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