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The D-term is one of the conserved charges of hadrons defined as the forward limit of the gravitational form factor D(t). We calculate the nucleon’s D-term in a holographic quantum chromodynamics model in which the nucleon is described as a soliton in five dimensions. We show that the form factor D(t) is saturated by the exchanges of infinitely many 0++ and 2++ glueballs dual to transverse-traceless metric fluctuations on the Wick-rotated AdS7 black hole geometry. We refer to this phenomenon as “glueball dominance,” in perfect analogy to the vector meson dominance of the electromagnetic form factors. However, the value at vanishing momentum transfer D(t = 0) can be interpreted as due to the exchange of pairs of pions and infinitely many vector and axial-vector mesons without any reference to glueballs. We find that the D-term is slightly negative as a result of a cancellation between the isovector and isoscalar meson contributions.

We study anomalies of fermions with spacetime dependent mass. Using Fujikawa's method, it is found that the anomalies associated with the $U(N)_+\times U(N)_-$ chiral symmetry and $U(N)$ flavor symmetry for even and odd dimensions, respectively, can be written in terms of superconnections. In particular, the anomaly for a vector-like $U(1)$ symmetry is given by the Chern character of the superconnection in both even and odd dimensional cases. It is also argued that the non-Abelian anomaly for a system in D-dimensional spacetime is characterized by a (D+2)-form part of the Chern character of the superconnection which generalizes the usual anomaly polynomial for the massless case. These results enable us to analyze anomalies in the systems with interfaces and spacetime boundaries in a unified way. Applications to index theorems, including Atiyah-Patodi-Singer index theorem and Callias-type index theorem, are also discussed. In addition, we give a natural string theory interpretation of these results., 50 pages, v2: minor improvements, an appendix and references are added

We analyze excited baryon states using a holographic dual of quantum chromodynamics that is defined on the basis of an intersecting D4/D8-brane system. Studies of baryons in this model have been made by regarding them as a topological soliton of a gauge theory on a five-dimensional curved spacetime. However, this allows one to obtain only a certain class of baryons. We attempt to present a framework such that a whole set of excited baryons can be treated in a systematic way. This is achieved by employing the original idea of Witten, which states that a baryon is described by a system composed of $N_c$ open strings emanating from a baryon vertex. We argue that this system can be formulated by an Atiyah–Drinfeld–Hitchin–Manin-type matrix model of Hashimoto–Iizuka–Yi together with an infinite tower of the open string massive modes. Using this setup, we work out the spectra of excited baryons and compare them with the experimental data. In particular, we derive a formula for the nucleon Regge trajectory assuming that the excited nucleons lying on the trajectory are characterized by the excitation of a single open string attached on the baryon vertex.

The $\mathbf{O}(D,D)$ covariant generalized metric, postulated as a truly fundamental variable, can describe novel geometries where the notion of Riemannian metric ceases to exist. Here we quantize a closed string upon such backgrounds and identify flat, anomaly-free, non-Riemannian string vacua in the familiar critical dimension, $D{=26}$ (or $D{=10}$). Remarkably, the whole BRST closed string spectrum is restricted to just one level with no tachyon, and matches the linearized equations of motion of Double Field Theory. Taken as an internal space, our non-Riemannian vacua may open up novel avenues alternative to traditional string compactification., Comment: 6 pages. [v2] comment/reference added, title changed from "Single Level String Theory", to appear in PRL

We study the vacuum structure of N_f flavour two-dimensional QED with an arbitrary integer charge k. We find that the axial symmetry is spontaneously broken from Z_(kN_f) to Z_(N_f) due to the non-vanishing condensate of a flavour singlet operator, resulting in k degenerate vacua. An explicit construction of the k vacua is given by using a non-commutative algebra obtained as a central extension of the Z_(kN_f) discrete axial symmetry and Z_k 1-form (center) symmetry, which represents the mixed 't Hooft anomaly between them. We then give a string theory realization of such a system with k=2 and N_f=8 by putting an anti D-string in the vicinity of an orientifold O1- plane and study its dynamics using the two-dimensional gauge theory realized on it. We calculate the potential between the anti D-string and the O1- plane and find repulsion in both weak and strong coupling regimes of the two dimensional gauge theory, corresponding to long and short distances, respectively. We also calculate the potential for the (Q,-1) string (the bound state of an anti D-string and Q fundamental strings) located close to the O1- plane. The result is non-perturbative in the string coupling., 38 pages, 3 eps figures. v2: minor corrections, refs. added. v3: minor corrections, figure added. Version to appear in JHEP

We study deformations of ${\cal N}=4$ supersymmetric Yang-Mills theory with space-time dependent couplings by embedding probe D3-branes in supergravity backgrounds with non-trivial fluxes. The effective action on the world-volume of the D3-branes is analyzed and a map between the deformation parameters and the fluxes is obtained. As an explicit example, we consider D3-branes in a background corresponding to $(p,q)$ 5-branes intersecting them and show that the effective theory on the D3-branes precisely agrees with the supersymmetric Janus configuration found by Gaiotto and Witten in arXiv:0804.2907 . D3-branes in an intersecting D3-brane background is also analyzed and the D3-brane effective action reproduces one of the supersymmetric configurations with $ISO(1,1)\times SO(2)\times SO(4)$ symmetry found in our previous paper arXiv:1710.09792 ., Comment: 36 pages

In the top-down holographic model of QCD based on D4/D8-branes in type IIA string theory and some of the bottom-up models, the low energy effective theory of mesons is described by a five-dimensional Yang-Mills-Chern-Simons theory in a certain curved background with two boundaries. The five-dimensional Chern-Simons term plays a crucial role in reproducing the correct chiral anomaly in four-dimensional massless QCD. However, there are some subtle ambiguities in the definition of the Chern-Simons term for the cases with topologically nontrivial gauge bundles, which include the configurations with baryons. In particular, for the cases with three flavors, it was pointed out by Hata and Murata that the naive Chern-Simons term does not lead to an important constraint on the baryon spectrum, which is needed to pick out the correct baryon spectrum observed in nature. In this paper, we propose a formulation of a well-defined Chern-Simons term which can be used for the cases with baryons, and show that it recovers the correct baryon constraint as well as the chiral anomaly in QCD.

We study deformations of ${\cal N}=4$ supersymmetric Yang-Mills theory with couplings and masses depending on space-time. The conditions to preserve part of the supersymmetry are derived and a lot of solutions of these conditions are found. The main example is the case with $ISO(1,1)\times SO(3)\times SO(3)$ symmetry, in which couplings, as well as masses and the theta parameter, can depend on two spatial coordinates. In the case $ISO(1,1)$ is enhanced to $ISO(1,2)$, it reproduces the supersymmetric Janus configuration found by Gaiotto and Witten. When $SO(3)\times SO(3)$ is enhanced to $SO(6)$, it agrees with the world-volume theory of D3-branes embedded in F-theory (a background with 7-branes in type IIB string theory). We also find the general solution of the supersymmetry conditions for the cases with $ISO(1,1)\times SO(2)\times SO(4)$ symmetry. The cases with time dependent couplings and/or masses are also considered., Comment: 48 pages, v2: minor corrections

We study SU(N) Yang-Mills-Chern-Simons theory in the presence of defects that shift the Chern-Simons level from a holographic point of view by embedding the system in string theory. The model is a D3-D7 system in Type IIB string theory, whose gravity dual is given by the AdS soliton background with probe D7-branes attaching to the AdS boundary along the defects. We holographically renormalize the free energy of the defect system with sources, from which we obtain the correlation functions for certain operators naturally associated to these defects. We find interesting phase transitions when the separation of the defects as well as the temperature are varied. We also discuss some implications for the Fractional Quantum Hall Effect and for two-dimensional QCD., Comment: 56 pages, 19 figures, v2: sign convention for CS level in terms of number of D7 branes switched, UV behavior of one and two point functions added in sec. 5.4.1 and 5.4.3, references added, typos corrected

In spite of intensive endeavor over decades, rigid and nonrigid factorizations under metric constraints, possibly in the presence of missing components, remain to be very challenging. In this work, we try to break the hard nut by generalizing to these problems the Wiberg algorithm, one of the most successful solutions for unconstrained bilinear factorization. To properly handle missing components, we advocate a bilinear factorization formulation with an extra mean vector. In spirit of the Wiberg algorithm, we first propose an efficient and initialization-insensitive algorithm for unconstrained factorization, posterior correction of whose solution offers reasonable initialization for metric upgrade. For factorization with metric constraints, we reformulate it into an unconstrained problem through quaternion parametrization, which merges elegantly into our unconstrained factorization algorithm. Extensive experiment results verify that our proposed methods are fast, accurate and robust to high percentage of missing components.

We give a very brief summary of the basic idea and some of the interesting results in holographic QCD. Using the gauge/string duality, we obtain a low energy effective theory of hadrons based on string theory. Mesons and baryons are obtained as open strings and D-branes, respectively, and a lot of properties of hadrons can be extracted using this new description.

A state-of-the-arts biped robot can take foot-steps such that its heels always overhang corner edges while ascending stairs, as humans naturally do. The overhanging footstep is advantageous in terms of relaxation of restrictions on gait planning. However, in a man-made environment without geometry information, the overhanging footstep requires the estimation of the exact step-edge position in real-time. In this paper we propose a real-time method for estimating step edge positions using stereo images. We find a straight edge line, which divides a view area into two regions representing the upper and lower step-able planes at the target edge. The edge line is obtained by minimizing a cost function composed of pixel-value-difference images, which are computed from the two stereo images and the geometry parameters of the planes, estimated by an efficient direct method in high precision. The validity of the proposed method is demonstrated through online experiments using stereo cameras mounted on the body of a biped robot traversing real stairs.

In this paper, we present a novel approach to imaging a panoramic (360°) environment and computing its dense depth map. Our approach adopts a multi-baseline stereo strategy using a set of multi-perspective panoramas where large baseline lengths are available. We design two image acquisition rigs for capturing such multi-perspective panoramas. The first one is composed of two parallel stereo cameras. By rotating the rig about a vertical axis, we generate four multi-perspective panoramas by resampling the regular perspective images captured by the stereo cameras. Then a depth map is estimated from the four multi-perspective panoramas and an original perspective image using a multi-baseline matching technique with different types of epipolar constraints. The second one is composed of a single camera and two mirrors. By rotating the rig, we acquire a spatio-temporal volume that is made up of the sequential images captured by the camera. Then we estimate a depth map by extracting trajectories from the spatio-temporal volume by using a multi-baseline stereo technique by considering occlusions. We can consider both rotating rigs as a single rotating camera with a very large field of view (FOV), that offers a large baseline length in depth estimation. In addition, compared with a previous approach using two multi-perspective panoramas from a single rotating camera, our approach can reduce matching errors due to image noise, repeated patterns, and occlusions by multi-baseline stereo techniques. Experimental results using both synthetic and real images show that our approach produces high quality panoramic 3D reconstruction.

There are two major approaches for estimating camera motion (egomotion) given an image sequence. Each approach has own strengths and weaknesses.

It is important for autonomous control of a biped robot to obtain the 3D information of the ground on which the robot walks. When a biped robot traverses a floor including slopes, sensors should be able to detect a slope and precisely measure the angle of the slope, along with the positions of its beginning and end. In this paper, we propose a realtime floor sensing method using stereo cameras mounted on a biped robot. We detect a slope in the environment and estimate the inclination angle and the boundary by fitting a set of plane parameter vectors to a two-plane model. For obtaining the parameter vector set, we first determine multiple regions of interest (ROI) in a reference image by using footstep positions up to several steps, scheduled by a current footstep plan. Then the parameter vector of the floor with respect to each ROI are efficiently and accurately estimated by a fast direct method with motion compensation. The fitting result is feedback for stable walking by updating the footstep plan . The validity of the proposed method is demonstrated through online experiments using stereo cameras mounted on the body of a biped robot, Honda ASIMO, traversing a real slope.

We propose a holographic dual of large N_c QCD with the gauge group O(N_c) and USp(N_c) and N_f flavors of massless quarks. This is constructed by adding O6-planes to an intersecting D4-D8 system in type IIA superstring theory. The holographic dual description is formulated in the Witten's D4-brane background with D8-branes and O6-planes embedded in it as probes. The D4-brane background gives rise to a smooth interpolation of D8-anti-D8 pairs and an O6-anti-O6 pair. We show that the resultant brane configuration explains geometrically the flavor symmetry breaking patterns in O(N_c) and USp(N_c) QCD that are caused by quark bilinear condensates. We next discuss that baryons can be realized as D4-anti-D4 pairs wrapped on S^4 that intersect with the O6-plane. By analyzing the tachyons on it, we reproduce the stability conditions of the baryons that are expected from the gauge theory viewpoint. The stable baryon configurations are classified systematically by using K-theory. We also give a similar analysis for the flux tubes and again reproduce the results that are consistent with QCD., Comment: 20 pages, 2 figures, v2: discussions of flux tubes clarified, references added, v3: minor changes, final version published in PTP

We give a brief summary of our recent works [H. Hata, T. Sakai, S. Sugimoto and S. Yamato, Prog. Theor. Phys. 117 (2007), 1157; hep-th/0701280. K. Hashimoto, T. Sakai and S. Sugimoto, arXiv:0806.3122] on the baryons in holographic QCD [T. Sakai and S. Sugimoto, Prog. Theor. Phys. 113 (2005), 843; hep-th/0412141; Prog. Theor. Phys. 114 (2005), 1083; hep-th/0507073]. In the holographic description, meson effective action is given by the five dimensional Yang-Mills – Chern-Simons theory in a certain curved background. The baryon is described as a soliton carrying an instanton number on the four dimensional space. By quantizing the soliton, we obtain various baryon states and calculate static quantities such as charge radii, magnetic moments, axial coupling, etc.