New Insights into Strongly Coupled Quantum Field Theories

In theoretical physics, researchers have shown interest in studying complex quantum field theories, particularly when they are strongly coupled. These theories can reveal important features of nature, such as confinement in Gauge Theories. However, traditional techniques often fail when these theories become strongly coupled. Over the last two decades, holography has emerged as a way to tackle this challenge. Holography links certain quantum field theories to gravity theories in higher dimensions. This connection allows scientists to glean insights into the behavior of strongly coupled quantum field theories by examining their gravitational counterparts. This fascinating relationship has opened new paths of research that link quantum gravity to supersymmetric quantum field theories.

Among various examples of strongly coupled field theories are the so-called Argyres-Douglas theories, which are found in four dimensions. These theories arise at special points in the moduli space of gauge theories, particularly where non-local dyons become massless. Such theories are inherently strongly coupled, making conventional approaches impractical. Despite their complexity, their existence is supported by both field and string theory arguments.

One noteworthy approach to these theories involves compactifying a six-dimensional theory on a sphere with two punctures. This configuration corresponds to M5-branes wrapping the punctured sphere. Such an approach provides a fresh way to investigate these theories using holography. Previous works have demonstrated that these theories can be analyzed using dual Supergravity solutions that resemble M5-branes wrapped on a two-dimensional disc.

The supergravity situations in question relate closely to M5-branes that are wrapped on surfaces of higher genus. However, the way these surfaces interact with supersymmetry differs from simpler cases with constant curvature metrics. This is due to the fact that discs and spindles don’t have metrics with constant curvature. Consequently, the preservation of supersymmetry requires unique mechanisms rather than a straightforward topological twist.

When considering spindles, supersymmetry can be sustained through two methods: the twist and the anti-twist. The twist method involves balancing total R-symmetry flux against the integrated curvature. The anti-twist is more complex since the total R-symmetry flux does not equal the curvature but still manages to preserve supersymmetry. Both methods share a common feature-R-symmetry interacts with the spindle's isometry. Similarly, in discs, R-symmetry and isometry mix to maintain supersymmetry. Here, the mechanism diverges from the anti-twist and uniquely suits the presence of punctures.

After establishing successful spindle and disc solutions, a logical question arises: can we extend wrapped brane solutions to higher-dimensional orbifolds? Previous works have explored this prospect, and our findings contribute to broadening the scope.

In this paper, we investigate aspects of the holographic duals of Argyres-Douglas theories. Initially, we discuss a puzzle concerning the global symmetries of these duals. Subsequently, we establish a truncation of seven-dimensional supergravity down to five-dimensional gauged supergravity, allowing us to explore a range of new supergravity solutions. These include solutions linked with M5-branes wrapping four-dimensional orbifolds.

Typically, Argyres-Douglas SCFTs exhibit a global symmetry tied to the superconformal R-symmetry. However, in holographic duals arising in supergravity backgrounds, two isometries are frequently present. The second isometry serves as a remnant of M5-branes smeared across a circle within the internal space. This smearing aligns with the expectations of Seiberg-Witten geometry, asserting that M5-branes should be separated near irregular punctures. Although this smeared arrangement is just a remnant of the supergravity description, contributions at lower orders are expected to clarify the smearing, leading to localized distributions of M5-branes along smeared directions. If the branes are localized, this breaks the additional symmetry, thereby yielding the correct quantity of global symmetries.

In the absence of this second symmetry, previous analyses have shown the necessity of an axion, which, through the Stuckelberg mechanism, bestows mass upon one of the gauge fields. This validates the breaking of the unwanted symmetry.

Given that this additional symmetry is non-essential and should be broken in a bona fide dual, we aim to illustrate this mechanism. The solutions we analyze can be generated by incorporating a scalar field that parallels the axion in the Stuckelberg mechanism. By tweaking the gauge field, we can absorb one degree of freedom into it, resulting in an effective local solution.

The local solution's discovery can be traced back to BPS bubbling solutions, albeit our findings present noteworthy differences in global aspects. An analytic continuation of these solutions leads to a non-compact two-dimensional surface. These solutions transition between specific geometries and asymptotic four-dimensional SCFTs, thereby identifying defects in the six-dimensional theory.

Transitioning from local solutions to a global framework remains intricate. In particular, we demonstrate the impossibility of locating backgrounds with added scalars that preserve compact internal spaces. While one can theoretically turn on two scalars, compactness requires both to be inactive. The non-compactness thus hinges on whether the coordinate ranges are bounded or not. Our analysis reveals compact solutions exist only when specific conditions are met, particularly when one endpoint aligns with a root of the range function, leading to simplified solutions.

We proceed to elevate our findings to eleven-dimensional supergravity, enabling us to compute various holographic observables. This includes central charges, anomalies, and the conformal dimensions of corresponding operators. These observables align perfectly across both duality sides in the limit of large parameters. Moreover, we scrutinize the internal geometry close to regular punctures, where the scalar field tends toward zero, reinstating symmetry. This local setting can be analyzed through electrostatics problems, although global completion often invalidates such transformations.

The latter part of the study shifts focus to alternative aspects of the Argyres-Douglas theories. Here, we delve into diverse solutions of seven-dimensional supergravity by permitting broader five-dimensional manifolds. These solutions contain various forms, some reflecting general state descriptions within Argyres-Douglas theories while others detail compactifications of these theories on diverse Riemann surfaces and orbifolds.

To derive these solutions, we build a truncation of seven-dimensional gauged supergravity down to five-dimensional Romans' gauged supergravity. This results in a consistent truncation, which allows us to draw connections between solutions in five and seven dimensions. In this framework, uncovering solutions within five-dimensional gauged supergravity tends to be more manageable than directly retrieving wrapped brane solutions in higher dimensions, granting access to richer data.

As an initial outcome, we could analyze asymptotically locally AdS solutions in Romans' supergravity, providing insight into high-energy regimes of dual SCFTs, including black hole backgrounds. Specifically, the Bekenstein-Hawking entropy of these black holes correlates directly with the superconformal index in dual theories. The rising interest in the thermodynamic and structural properties of these AdS black holes underscores such alignments.

Secondly, our truncation permits the identification of new solutions that correspond to M5-branes wrapped on broader orbifolds. Research has demonstrated that there are more extensive means of upholding supersymmetry on two-dimensional spaces with conical defects, leading us to investigate how these principles extend to higher-dimensional orbifolds. Our findings reveal that local solutions can be interpreted as stacks of M5-branes wrapped around four-dimensional orbifolds.

Specific behaviors of these solutions depend on the parameter space, where the disc appears non-trivially fibred. This ultimately describes M5-branes that wrap genuine four-dimensional orbifolds. For a defined set of solutions, the fibration emerges as trivial, resulting in a factorized representation of M5-branes.

This research aims to achieve two primary objectives. First, we presented new solutions by integrating a scalar into existing disc solutions. These solutions offer explicit examples of how unwanted symmetry can be disrupted in original backgrounds. Secondly, we initiated a study of fresh solutions that relate to generalized states within Argyres-Douglas theories and M5-branes wrapping four-dimensional surfaces. As a result, these four-dimensional spaces arise as fibered discs over another disc or spindle.

The implications of this work are vast, providing numerous future research avenues. For instance, there could be an extension of our findings to encompass M2, D3, or D4 branes that wrap discs or spindles. The local solutions could arise from analytic continuations, prompting inquiries into which solutions permit global completion. Another area of interest is the relationship between dual SCFTs and specific solutions, particularly regarding D3 branes.

Further analysis indicates that extra scalars might not be applicable when dealing with spindle-wrapped M5-branes. This implies genuine global symmetries persist within these theories. Moreover, by examining various solutions, we can unlock new avenues within the framework of the Toda equation defining a higher-dimensional background.

Studying surface defects in the theory provides additional opportunities. The solutions presented offer potential for more general conformal surface defects. Exploring these dynamics could yield valuable insights into aspects of existing SCFTs.

In conclusion, this work lays the groundwork for exploring M-theory through the lens of novel solutions. By bridging the gaps between theories and solutions, we aim to provide a comprehensive understanding of supersymmetric field theories and their dual counterparts.