One-loop surface tensions of (supersymmetric) kink domain walls from dimensional regularization

We consider domain walls obtained by embedding the 1+1-dimensional $\phi^4$-kink in higher dimensions. We show that a suitably adapted dimensional regularization method avoids the intricacies found in other regularization schemes in both supersymmetric and non-supersymmetric theories. This method allows us to calculate the one-loop quantum mass of kinks and surface tensions of kink domain walls in a very simple manner, yielding a compact d-dimensional formula which reproduces many of the previous results in the literature. Among the new results is the nontrivial one-loop correction to the surface tension of a 2+1 dimensional N=1 supersymmetric kink domain wall with chiral domain-wall fermions.Comment: 23 pages, LATeX; v2: 25 pages, 2 references added, extended discussion of renormalization schemes which dispels apparent contradiction with previous result

Local Casimir Energy For Solitons

Direct calculation of the one-loop contributions to the energy density of bosonic and supersymmetric phi-to-the-fourth kinks exhibits: (1) Local mode regularization. Requiring the mode density in the kink and the trivial sectors to be equal at each point in space yields the anomalous part of the energy density. (2) Phase space factorization. A striking position-momentum factorization for reflectionless potentials gives the non-anomalous energy density a simple relation to that for the bound state. For the supersymmetric kink, our expression for the energy density (both the anomalous and non-anomalous parts) agrees with the published central charge density, whose anomalous part we also compute directly by point-splitting regularization. Finally we show that, for a scalar field with arbitrary scalar background potential in one space dimension, point-splitting regularization implies local mode regularization of the Casimir energy density.Comment: 18 pages. Numerous new clarifications and additions, of which the most important may be the direct derivation of local mode regularization from point-splitting regularization for the bosonic kink in 1+1 dimension

Mode regularization of the susy sphaleron and kink: zero modes and discrete gauge symmetry

To obtain the one-loop corrections to the mass of a kink by mode regularization, one may take one-half the result for the mass of a widely separated kink-antikink (or sphaleron) system, where the two bosonic zero modes count as two degrees of freedom, but the two fermionic zero modes as only one degree of freedom in the sums over modes. For a single kink, there is one bosonic zero mode degree of freedom, but it is necessary to average over four sets of fermionic boundary conditions in order (i) to preserve the fermionic Z$_2$ gauge invariance $\psi \to -\psi$, (ii) to satisfy the basic principle of mode regularization that the boundary conditions in the trivial and the kink sector should be the same, (iii) in order that the energy stored at the boundaries cancels and (iv) to avoid obtaining a finite, uniformly distributed energy which would violate cluster decomposition. The average number of fermionic zero-energy degrees of freedom in the presence of the kink is then indeed 1/2. For boundary conditions leading to only one fermionic zero-energy solution, the Z$_2$ gauge invariance identifies two seemingly distinct `vacua' as the same physical ground state, and the single fermionic zero-energy solution does not correspond to a degree of freedom. Other boundary conditions lead to two spatially separated $\omega \sim 0$ solutions, corresponding to one (spatially delocalized) degree of freedom. This nonlocality is consistent with the principle of cluster decomposition for correlators of observables.Comment: 32 pages, 5 figure

Nonvanishing quantum corrections to the mass and central charge of the N=2 vortex and BPS saturation

The one-loop quantum corrections to the mass and central charge of the N=2 vortex in 2+1 dimensions are determined using supersymmetry-preserving dimensional regularization by dimensional reduction of the corresponding N=1 model with Fayet-Iliopoulos term in 3+1 dimensions. Both the mass and the central charge turn out to have nonvanishing one-loop corrections which however are equal and thus saturate the Bogomolnyi bound. We explain BPS saturation by standard multiplet shortening arguments, correcting a previous claim in the literature postulating the presence of a second degenerate short multiplet at the quantum level.Comment: 1+16 pages LATeX, 1 figure. v3: minor addition

The anomaly in the central charge of the supersymmetric kink from dimensional regularization and reduction

We show that the anomalous contribution to the central charge of the 1+1-dimensional N=1 supersymmetric kink that is required for BPS saturation at the quantum level can be linked to an analogous term in the extra momentum operator of a 2+1-dimensional kink domain wall with spontaneous parity violation and chiral domain wall fermions. In the quantization of the domain wall, BPS saturation is preserved by nonvanishing quantum corrections to the momentum density in the extra space dimension. Dimensional reduction from 2+1 to 1+1 dimensions preserves the unbroken N=1/2 supersymmetry and turns these parity-violating contributions into the anomaly of the central charge of the supersymmetric kink. On the other hand, standard dimensional regularization by dimensional reduction from 1 to (1-epsilon) spatial dimensions, which also preserves supersymmetry, obtains the anomaly from an evanescent counterterm.Comment: LATeX, 19 pages, v2: significantly extended section 4 on dimensional reduction and evanescent counterterm

Алгоритм нормального ортогонального преобразования двумерного образа

В статті на базі алгоритму формування матричного оператора дискретного ортогонального одновимірного перетворення створено алгоритм двовимірного перетворення. Проблема створення двовимірного перетворення полягає в великому порядку матричного оператора, якщо двовимірний образ представляється у вигляді одного рядка, утвореного послідовністю рядків (стовпців) образу. В цьому випадку для матриці образу порядку N порядок матричного оператора становить N2, тобто кількість елементів такого оператора дорівнює N4, що неприпустимо, враховуючи, що для образів N = 256…1024. Отримано просту структуру формування матричного оператора дискретного двовимірного перетворення, урахування якої дозволяє зменшити об’єм пам’яті, необхідної для обчислення коефіцієнта трансформант, до N3, що робить можливим класифікацію образів з матрицями порядку N ≈ 256…1024. Алгоритм проілюстровано на прикладі, обраному виходячи з міркувань простоти перевірки отримуваних результатів.A new 2D transformation algorithm based on algorithm of matrix operator formation in 1D discrete orthogonal transformation is presented. Complexity 2D algorithm creation is a high order of matrix operator when 2D image is presented as a sequence of rows (columns). In this case the order of matrix operator is N2 for image matrix of N order. As result, the number of its elements is equal to N4, which is equivalent of huge figure for image, having size N = 256…1024. A simple algorithm for creation of matrix operator in 2D discrete transformation was obtained. It allows reduce to N3 the memory volume, required for transform coefficient calculation. It makes possible to classify images having matrix of order N ≈ 256…1024. The algorithm is illustrated on the example selected from the ease of inspection results.В статье на базе алгоритма формирования матричного оператора дискретного ортогонального одномерного преобразования создан алгоритм двумерного преобразования. Проблема создания двумерного преобразования состоит в большом порядке матричного оператора, если двумерный образ представить в виде одной строки, образованной последовательностью строк (столбцов) образа. В этом случае для матрицы образа порядка N порядок матричного оператора равен N2, т.е. количество элементов матричного оператора равно N4, что недопустимо, учитывая, что для образов N = 256…1024. Получена простая структура формирования матричного оператора двумерного дискретного преобразования, учет которой позволяет уменьшить объем памяти, необходимой для вычисления коэффициента трансформант, до N3, что делает возможным классификацию образов с матрицами порядка N ≈ 256…1024. Алгоритм проиллюстрирован на примере, выбранном исходя из простоты проверки получаемых результатов

Theoretical Overview: The New Mesons

After commenting on the state of contemporary hadronic physics and spectroscopy, I highlight four areas where the action is: searching for the relevant degrees of freedom, mesons with beauty and charm, chiral symmetry and the D_{sJ} levels, and X(3872) and the lost tribes of charmonium.Comment: 10 pages, uses jpconf.cls; talk at First Meeting of the APS Topical Group on Hadronic Physic