D-brane Probes Research Articles

Duality walls, duality trees and fractional branes

In this paper, we compute the NSVZ beta functions for [Formula: see text] four-dimensional quiver theories arising from D-brane probes on singularities, complete with anomalous dimensions, for a large set of phases in the corresponding duality tree. While these beta functions are zero for D-brane probes, they are nonzero in the presence of fractional branes. As a result there is a nontrivial RG behavior. We apply this running of gauge couplings to some toric singularities such as the cones over Hirzebruch and del Pezzo surfaces. We observe the emergence in string theory, of “Duality Walls,” a finite energy scale at which the number of degrees of freedom becomes infinite and beyond which Seiberg duality does not proceed. We also identify certain quiver symmetries as T-duality-like actions in the dual holographic theory.

On co-dimension 2 defect anomalies in N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 4 SYM and (2,0) theory via brane probes in AdS/CFT

We consider a 12\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\frac{1}{2} $$\\end{document}-BPS solution for a D3 brane probe in AdS5× S5 that has world-volume geometry of AdS3× S1. It intersects the boundary over a surface that represents a dimension 2 defect in the boundary N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 4 SYM theory. The effective action of the probe brane is proportional to the logarithmically divergent volume of AdS3 and may thus be interpreted as computing conformal anomaly of supersymmetric S2 defect. The classical action scales as N. We compute the 1-loop correction to it due to quantum fluctuations of the D3 brane world-volume fields and compare the result to an earlier suggested expression for the defect anomaly. We also perform a similar analysis of a 12\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\frac{1}{2} $$\\end{document}-BPS M5 brane probe solution in AdS7× S4 with the world-volume geometry of AdS5× S1 that represents a dimension 4 defect in the boundary (2,0) 6d theory. Here the classical M5 brane action computes the leading order N2 term in a-anomaly of the supersymmetric S4 defect. We perform a detailed computation of the 1-loop correction to the M5 brane effective action and thus provide a prediction for the subleading constant in the S4 defect a-anomaly coefficient.

D-terms in generalised complex geometry

Generalised Complex Geometry provides a natural interpretation of the N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 1 supersymmetry conditions for warped solutions of type II supergravity as differential equations on polyforms on the internal manifold. Written in this language the supersymmetry conditions correspond to calibration conditions for probe D-branes: D-string, domain-wall or space-filling branes, depending on the directions they span in the non-compact four-dimensional space. The BPS condition corresponding to the calibration of space-filling D-branes has been reformulated by Tomasiello, eliminating the explicit dependence on the metric. We generalise this derivation to the case of non-supersymmetric backgrounds violating the domain-wall and D-string calibration conditions. We use this reformulation to derive constraints that the ten-dimensional solutions with BPS space-filling sources must respect in order to dimensionally reduce to solutions of four-dimensional N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 1 supergravity with non-vanishing F-terms and potentially non-vanishing D-terms. We give the equations of motion for the class of type II vacua satisfying these constraints in the language of pure spinors. We investigate how restrictive these constraints are for the class of type IIB SU(3) backgrounds with BPS space-filling O5-planes.

Thermodynamics of black holes with probe D-branes

Understanding how the thermodynamic properties of a black hole are modified when probed by D-branes is an important problem in AdS/CFT. This work focuses on a recently proposed black hole/D3-brane system in AdS5×S5, which is dual to four-dimensional N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 4 SYM in the presence of a two-dimensional surface defect. The Laplace transform that extracts the asymptotic growth of states in this defect CFT naturally defines a thermodynamic approach in the gravitational side of the duality for which charges and entropy are real. Studying the superconformal defect index in a large-charge expansion for all values of N, we compute the leading correction to the entropy of the combined system, which matches precisely with its gravity counterpart.

The conformal manifold of S-folds in string theory

We continue the holographic exploration of the conformal manifold of 3d N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 2 S-fold SCFTs constructed by gauging the flavor symmetry of the Gaiotto-Witten T[U(N)] theory. We show how to uplift the two-parameter family of AdS4 vacua dual to this conformal manifold to 10d backgrounds of type IIB supergravity. We use these uplifted solutions to shed new light on the mysterious nature of the infinite distance limit on the conformal manifold and to study probe strings and D3-branes. This analysis uncovers an intriguing structure of the S3 partition function of the S-fold SCFTs which resembles the giant graviton expansion of the superconformal index of 4d N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 4 SYM. We also show how to each member of the family of supersymmetric AdS4 vacua one can associate a consistent truncation to 4d N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 2 gauged supergravity and use this result, in conjunction with holography, to calculate the large N partition function of the 3d S-fold SCFT on compact Euclidean manifolds. Finally, we generalize the supersymmetric AdS4 vacua to a four-parameter family of non-supersymmetric AdS4 solutions.

Holographic Schwinger effect in spinning black hole backgrounds* *Supported by the National Natural Science Foundation of China (NSFC) (12375140) and the Fundamental Research Funds for the Central Universities, China University of Geosciences (Wuhan) (G1323523064)

We perform a potential analysis for the holographic Schwinger effect in spinning Myers-Perry black holes. We compute the potential between the produced pair by evaluating the classical action of a string attached on a probe D3-brane at an intermediate position in the AdS bulk. We find that increasing the angular momentum reduces the potential barrier, thus enhancing the Schwinger effect, consistent with previous findings obtained via the local Lorentz transformation. In particular, these effects are more visible for the particle pair lying in the transversal plane compared with that along the longitudinal orientation. In addition, we discuss how the Schwinger effect changes with the shear viscosity to entropy density ratio at strong coupling under the influence of angular momentum.

Probing supersymmetric black holes with surface defects

It has long been conjectured that the large N deconfinement phase transition of mathcal{N} = 4 SU(N) super-Yang-Mills corresponds via AdS/CFT to the Hawking-Page transition in which black holes dominate the thermal ensemble, and quantitative evidence of this has come through the recent matching of the superconformal index of frac{1}{16} -BPS states to the supersymmetric black hole entropy. We introduce the half-BPS Gukov-Witten surface defect as a probe of the superconformal index, which also serves as an order parameter for the deconfinement transition. This can be studied directly in field theory as a modification of the usual unitary matrix model or in the dual description as a D3-brane probe in the background of a (complex) supersymmetric black hole. Using a saddle point approximation, we determine our defect index in the large N limit as a simple function of the chemical potentials and show independently that it is reproduced by the renormalized action of the brane in the black hole background. Along the way, we also comment on the Cardy limit and the thermodynamics of the D3-brane in the generalized ensemble. The defect index sharply distinguishes between the confining and the deconfining phases of the gauge theory and thus is a supersymmetric non-perturbative order parameter for these large N phase transitions which deserves further investigation. Finally, our work provides an example where the properties of a black hole coupled to an external system can be analyzed precisely.

Holographic Schwinger Effect with a Rotating Probe D3-Brane

This paper, among other things, talks about possible research on the holographic Schwinger effect with a rotating probe D3-brane. We discover that for the zero temperature case in the Schwinger effect, the faster the angular velocity and the farther the distance of the test particle pair at D3-brane, the potential barrier of total potential energy also grows higher and wider. This paper shows that at a finite temperature, when S5 without rotation is close to the horizon, the Schwinger effect fails because the particles remain in an annihilate state, which is an absolute vacuum state. However, the angular velocity in S5 will avoid the existence of an absolute vacuum near the horizon. For both zero and finite temperature states, the achieved results completely agree with the results of the Dirac-Born-Infeld (DBI) action. So the theories in this paper are consistent. All of these show that these theories will play important roles in future pair production research.

Phases of a 10-D holographic hard wall model

In this article, we study the finite temperature properties of a 10-D version of a hardwall model for QCD. Introducing fundamental matter via probe D7-branes and separate cutoffs rm and rg for the branes and the bulk, we present a detailed exploration of the phases for varying temperature and quark mass. Finite thermodynamic quantities are calculated using the procedure of holographic renormalization and used to characterize the phases. Finally, by fitting glueball and vector meson masses, we show how a unique phase diagram can be isolated.

Holographic Schwinger effect and electric instability with anisotropy

According to the gauge-gravity duality, we systematically study the Schwinger effect and electric instability with anisotropy in a top-down holographic approach. The anisotropic black brane and bubble (soliton) background in IIB supergravity are employed and the dual theories in these backgrounds are expected to be anisotropic theory at finite temperature and anisotropic theory with confinement respectively. Then performing the potential analysis, we find due to the anisotropy, the potential barrier behaves oppositely with parallel and perpendicular electric fields, and this behavior agrees with the previous study about the quark potential with anisotropy in this system. Afterwards, we evaluate the pair production rate by solving the equation of motion for a fundamental string numerically which reveals the consistent behavior with the potential analysis. Furthermore, the probe D7-brane as flavor is introduced into the bulk in order to investigate the electric instability. The vacuum decay rate can be obtained by evaluating the imaginary part of the D7-brane action which again agrees with our potential analysis. Solving the associated constraint of gauge field strength on the flavor brane, we finally obtain the V-A curve displaying the distinct behavior of the conductivity in parallel and perpendicular direction which is in agreement with some bottom-up and phenomenologically holographic approaches in anisotropic fluid. Accordingly, we believe this work may be remarkable to study the electric features in strongly coupled anisotropic system.

Extra W-boson mass from a D3-brane

Motivated by the recent CDF measurement of the W-boson mass, we study string-based particle physics models which can accommodate this deviation from the Standard Model. We consider an F-theory GUT in which the visible sector is realized on intersecting 7-branes, and extra sector states arise from a probe D3-brane near an E-type Yukawa point. The D3-brane worldvolume naturally realizes a strongly coupled sector which mixes with the Higgs. In the limit where some extra sector states get their mass solely from Higgs vevs, this leads to a contribution to the ρ parameter which is too large, but as the D3-brane is separated from the 7-brane stack, this effect is suppressed, leading to O(1) - O(10) TeV scale extra sector states and a correction to ρ which would be in accord with the CDF result. We also estimate the contribution to the oblique electroweak parameter S, and find that it is compatible with existing constraints. This also leads to additional signatures, including diphoton resonances (as well as other diboson final states) in the O(1) - O(10) TeV range.

Comments on holographic level/rank dualities

We investigate a holographic realization in Type-IIB string theory of pure Chern-Simons theories, and focus on the level/rank dualities that they enjoy. The level/rank duality is established between the boundary theory, engineered utilizing D3-branes compactified on a S1, and the theory on probe D7-branes located at a specific bulk location. Paying attention to the boundary conditions imposed on the Ramond-Ramond (RR) two- and six-forms, we show that holography precisely reproduces several different level/rank dual pairs. The SL(2,Z) action relating all these theories is realized through the SL(2,Z) electric/magnetic duality involving the RR potentials.

Mapping out the internal space in AdS/BCFT with Wilson loops

We study Wilson loops in string theory realizations of AdS/BCFT and wedge holography. The field theories are based on 3d mathcal{N} = 4 long quiver gauge theories engineered by D3, D5 and NS5 branes, and on BCFTs involving 4d mathcal{N} = 4 SYM coupled to such 3d theories. The holographic duals have geometry AdS4× S2× S2 warped over a strip. We identify the holographic representation of antisymmetric Wilson loops associated with individual 3d gauge nodes in terms of probe D5-branes. The expectation values obtained holographically are matched to supersymmetric localization computations. Our results yield an identification of regions in the internal space with individual 3d gauge nodes. Connecting to bottom-up braneworld models, this gives a concrete notion of which parts of the 10d solutions correspond to the end-of-the-world brane and which to the remaining bulk. We also construct supersymmetric Janus on the brane embeddings in AdS5×S5, which describe surface defects with boundaries and interfaces in mathcal{N} = 4 SYM.

Domain wall AdS/QCD

We construct a new holographic description of QCD using domain wall fermions. The construction consists of probe D7 branes in a D5 brane geometry describing quarks on a 4+1d defect in a 5+1d gauge theory. We then compactify one dimension of the D5 to introduce confinement in the gauge degrees of freedom. In addition we allow a spatial dependent mass term for the D7 brane quarks to isolate chiral fermions on 3+1d domain walls. The D7 world volume fields, when restricted to the domain wall position, provide an AdS/QCD description. We compute the spectrum and compare to data. We include higher dimension operators to systematically improve the description.

Risking your NEC

Energy conditions, especially the null energy condition (NEC), are generically imposed on solutions to retain a physically sensible classical field theory and they also play an important role in the AdS/CFT duality. Using this duality, we study non-trivially deformed strongly coupled quantum field theories at large-Nc. The corresponding dual classical gravity constructions entail the use of radially non-monotonic D-brane distributions. The distributions are phenomenological in the sense that they do not correspond to the smearing of known probe D-brane embeddings. The gravity backgrounds are supersymmetric and hence perturbatively stable, and do not possess curvature singularities. There are no short-cuts through the bulk spacetime for signal propagation which assures that the field theory duals are causal. Nevertheless, some of our solutions violate the NEC in the gravity dual. In these cases the non-monotonicity of the D-brane distributions is reflected in the properties of the renormalization group flow: none of the c-functions proposed in the literature are monotonic. This further suggests that the non-monotonic behavior of the c-functions within previously known anisotropic backgrounds does not originate from the breaking of Lorentz invariance. We surmise that NEC violations induced by quantum corrections also need to be considered in holographic duals, but can be studied already at the classical level.

D5-brane in AdS black holes with nonzero gauge flux

We find the probe D5-brane solution on the black hole space–time which is asymptomatically [Formula: see text]. These black holes have spherical, hyperbolic and toroidal structures. Depending on the gauge flux on the D5-brane, the D5-brane behaves differently. By adding the fundamental string, the potential energy of the interface solution and the Wilson loop is given in the case of nonzero gauge flux.

Holographic Coulomb branch solitons, quasinormal modes, and black holes

Four-dimensional mathcal{N} = 4 supersymmetric Yang-Mills theory, at a point on the Coulomb branch where SU(N) gauge symmetry is spontaneously broken to SU(N − 1) × U(1), admits BPS solitons describing a spherical shell of electric and/or magnetic charges enclosing a region of unbroken gauge symmetry. These solitons have been proposed as gauge theory models for certain features of asymptotically flat extremal black holes. In the ’t Hooft large N limit with large ’t Hooft coupling, these solitons are holographically dual to certain probe D3-branes in the AdS5 × S5 solution of type IIB supergravity. By studying linearised perturbations of these D3-branes, we show that the solitons support quasinormal modes with a spectrum of frequencies sharing both qualitative and quantitative features with asymptotically flat extremal black holes.

Four-dimensional N = 1 theories, S-fold constraints on T-branes, and behaviors in IR and UV

We analyze four-dimensional (4d) N = 1 superconformal field theories (SCFTs) obtained as deformations of 4d N = 2 SCFTs on S-folds by tilting 7-branes. Geometric compatibility with the structures of S-folds constrains the forms of T-branes. As a result, brane monodromies are constrained. We also discuss two 4d N = 1 theories on probe D3-branes, where the two theories behave identically in IR, but they originate from different theories in UV. Studying the global structure of their geometry is useful in constructing these two theories.

Electromagnetic duality and D3-brane scattering amplitudes beyond leading order

We use on-shell methods to study the non-supersymmetric and supersymmetric low-energy S-matrix on a probe D3-brane, including both the 1-loop contributions of massless states as well as the effects of higher-derivative operators. Our results include: (1) A derivation of the duality invariance of Born-Infeld electrodynamics as the dimensional oxidation of the group of spatial rotations transverse to a probe M2-brane; this is done using a novel implementation of subtracted on-shell recursion. (2) The first explicit loop-level BCJ double-copy in a non-gravitational model, namely the calculation of the 4-point self-dual amplitude of non-supersymmetric Born-Infeld. (3) From previous results for n-point self-dual 1-loop BI amplitudes and the conjectured dimension-shifting relations in Yang-Mills, we obtain an explicit all-multiplicity, at all orders in E, expression for the 1-loop integrand of the MHV sector of mathcal{N} = 4 DBI. (4) For all n > 4, the explicitly integrated duality-violating 1-loop amplitudes (self-dual and next-to-self-dual in pure BI as well as MHV in mathcal{N} = 4 DBI) are shown to be removable at mathcal{O}left({upepsilon}^0right) by adding finite local counterterms; we propose that this may be true more generally at 1-loop order. (5) We find that in non-supersymmetric Born-Infeld, not all finite local counterterms needed to restore electromagnetic duality can be constructed using the double-copy with higher-derivative corrections, suggesting a fundamental tension between electromagnetic duality and color-kinematics duality at loop-level. Finally we comment on oxidation of duality symmetries in supergravity and the parallels it has to the M2-brane to D3-brane oxidation demonstrated in this paper.

Surface defects in holographic 5d SCFTs

We use holography to study codimension-2 surface defects in 5d SCFTs engineered by (p, q) 5-brane webs. The three-dimensional defects are realized by D3-branes ending on the brane web. We identify the holographic representation of the defects in Type IIB AdS6 solutions as probe D3-branes, and study conformal and non-conformal defects which, respectively, preserve one half and one quarter of the supersymmetry. For a sample of 5d SCFTs, including the TN theories, we provide explicit solutions for conformal and non-conformal defects. For the conformal defects we obtain their contribution to the free energy on S5.