非平凡插值函数h（λ）的存在性是包含ABJM理论的新AdS 4/CFT 3对应的新特征之一.在强耦合下，迄今为止，大多数半经典效应的研究都是针对AdS 4扇区的弦。已经提出了几种截断处方，导致对展开式h（λ）= \sqrt{λ/2} + c +.中常数项的不同预测。.我们计算了巨磁振子的量子修正，使用的代数曲线，并通过比较色散关系表明，相同的处方导致相同的C值在这个CP 3部门。然后，我们转向有限J效应，其中与Luescher F项校正的比较显示三个总和处方之一不匹配。我们还计算了一些双音和更高的F-条款为未来的比较。
英文摘要：
The existence of a nontrivial interpolating function h(λ) is one of the novel features of the new AdS4/CFT3 correspondence involving ABJM theory. At strong coupling, most of the investigation of semiclassical effects so far has been for strings in the AdS4 sector. Several cutoff prescriptions have been proposed, leading to different predictions for the constant term in the expansion h(λ)=\sqrt{λ/2} + c + ... . We calculate quantum corrections for giant magnons, using the algebraic curve, and show by comparing to the dispersion relation that the same prescriptions lead to the same values of c in this CP3 sector. We then turn to finite-J effects, where a comparison with the Luescher F-term correction shows a mismatch for one of the three sum prescriptions. We also compute some dyonic and higher F-terms for future comparisons.
We study up to 8-derivative terms in the Coulomb branch effective action of (1,1) little string theory, by collecting results of 4-gluon scattering amplitudes from both perturbative 6D super-Yang-Mills theory up to 4-loop order, and tree-level double scaled little string theory (DSLST). In previous work we have matched the 6-derivative term from the 6D gauge theory to DSLST, indicating that this term is protected on the entire Coulomb branch. The 8-derivative term, on the other hand, is unprotected. In this paper we compute the 8-derivative term by interpolating from the two limits, near the o…
We study the dynamics of non-Abelian vortex strings supported in ${\mathcal N}=2$ supersymmetric QCD with the U$(N)$ gauge group and $N_f=N$ quark flavors deformed by the mass $μ$ of the adjoint matter. In the limit of large $μ$ the bulk four-dimensional theory flows to ${\mathcal N}=1$ supersymmetric QCD. The dynamics of orientational zero modes of the non-Abelian string is described by the world sheet CP$(N-1)$ model. At $μ=0$ this model has ${\mathcal N}= \left(2,2\right) $ supersymmetry while at large $μ$ it flows to the non-supersymmetric CP$(N-1)$ model. We solve the world sheet model in…
A few nine-dimensional interpolating models with two parameters are constructed and the massless spectra are studied by considering compactification of heterotic strings on a twisted circle with Wilson line. It is found that there are some conditions between radius R and Wilson line A under which the gauge symmetry is enhanced. In particular, when the gauge symmetry is enhanced to SO(18) \times SO(14), the cosmological constant is exponentially suppressed. We also construct a non-supersymmetric string model which is tachyon-free in all regions of moduli space and whose gauge symmetry involves …
We consider time dependent backgrounds with a time-like linear dilaton which leads to a weakly coupled theory at asymptotic future known as the Supercritical Linear Dilaton (SCLD) phase. Even after projecting out the tachyon there are naive divergences in the partition function due to the spectrum of relevant deformations. Although the partition function seems divergent, the background is actually well defined in the far future due to vanishing backreactions, provided we start from an appropriate initial state called the "capping" state. We use the technique of interpolating functions to const…
The interpolation from supersymmetric to non-supersymmetric heterotic theories is studied, via the Scherk-Schwarz compactification of supersymmetric 6D theories to 4D. A general modular-invariant Scherk-Schwarz deformation is deduced from the properties of the 6D theories at the endpoints, which significantly extends previously known examples. This wider class of non-supersymmetric 4D theories opens up new possibilities for model building. The full one-loop cosmological constant of such theories is studied as a function of compactification radius for a number of cases, and the following interp…
We construct two interpolating solutions in type II string theory which interpolate between an AdS$_5$ in the UV and a hyperscaling violating three (spatial) dimensional Lifshitz space-time in the IR. The first solution is non-supersymmetric and is obtained from a known intersecting non-supersymmetric D3-brane with chargeless D0-brane solution of type IIB string theory, by restricting some parameters characterizing the solution and going to a new coordinate. In the IR the dilaton is non-constant in general and the metric is three (spatial) dimensional hyperscaling violating Lifshitz with dynam…
We propose an extension of natural inflation, where the inflaton potential is a general periodic function. Specifically, we study elliptic inflation where the inflaton potential is given by Jacobi elliptic functions, Jacobi theta functions or the Dedekind eta function, which appear in gauge and Yukawa couplings in the string theories compactified on toroidal backgrounds. We show that in the first two cases the predicted values of the spectral index and the tensor-to-scalar ratio interpolate from natural inflation to exponential inflation such as $R^2$- and Higgs inflation and brane inflation, …
It is known from the work in \cite{Lu:2007bu} of Lu et. al. that the non-supersymmetric charged D3-brane (with anisotropies in time as well as one of the spatial directions of D3-brane) of type IIB string theory is characterized by five independent parameters. By fixing one of the parameters and zooming into a particular region of space-time we construct a four parameter family of solution in AdS$_5$, which interpolates between AdS$_5$ black hole and AdS$_5$ soliton (when one of spatial directions in the Poincare coordinates is compact) by continuously changing the parameters (there is no need…
Based on the recent indications of integrability in the planar ABJ model, we conjecture an exact expression for the interpolating function h(λ_1,λ_2) in this theory. Our conjecture is based on the observation that the integrability structure of the ABJM theory given by its Quantum Spectral Curve is very rigid and does not allow for a simple consistent modification. Under this assumption, we revised the previous comparison of localization results and exact all loop integrability calculations done for the ABJM theory by one of the authors and Grigory Sizov, fixing h(λ_1,λ_2). We checked our conj…
The instant form and the front form of relativistic dynamics proposed by Dirac in 1949 can be linked by an interpolation angle parameter $δ$ spanning between the instant form dynamics (IFD) at $δ=0$ and the front form dynamics which is now known as the light-front dynamics (LFD) at $δ=π/4$. We present the formal derivation of the interpolating quantum electrodynamics (QED) in the canonical field theory approach and discuss the constraint fermion degree of freedom which appears uniquely in the LFD. The constraint component of the fermion degrees of freedom in LFD results in the instantaneous co…
We study the BPS counting functions (free energies) of the M-string configurations. We consider separated M5-branes along with M2-branes stretched between them, with M5-branes acting as domain walls interpolating different configurations of M2-branes. We find recursive structure in the free energies of these configurations. The M-string degrees of freedom on the domain walls are interpreted in terms of a pair of interacting supersymmetric WZW models. We also compute the elliptic genus of the M-string in a toy model of the ABJM theory and compare it with the M-theory computation.
We calculate the two-loop correction to the dispersion relation for worldsheet modes of the BMN string in AdS(n) x S(n) x T(10-2n) for n=2,3,5. For the massive modes the result agrees with the exact dispersion relation derived from symmetry considerations with no correction to the interpolating function h. For the massless modes in AdS(3) x S(3) x T(4) however our result does not match what one expects from the corresponding symmetry based analysis. We also derive the S-matrix for massless modes up to the one-loop order. The scattering phase is given by the massless limit of the Hernandez-Lope…
Finite-size corrections for quantum strings on AdS_4 x CP^3
我们重新计算了在arXiv：0807.1527中开始的对AdS_4 x CP^3上IIA型弦态pp波能量的曲率修正。利用arXiv：0912.2257中的近pp波哈密顿量，我们计算了一组1/R^2阶玻色弦态能量的第一个非零修正，其中R是背景的曲率半径。主要的曲率修正在汉密尔顿中产生了三次项（1/R阶）和四次项（1/R^2阶），我们对此实施了适当的正常排序规定。考虑到所有可能的费米子和玻色子弦态的贡献，我们发现模数之和存在对数偏差，从而抵消了三次和四次Hamilton量。我们表明，立方哈密顿量自然要求的截止求和重模式必须是轻模式的两倍。在此条件下，进入磁振子色散关系的强弱耦合插值函数h（λ）不受单圈修正，与代数曲线谱一致。然而，单磁振子色散关系表现出有限尺寸的指数修正。
In theoretical physics, we sometimes have two perturbative expansions of physical quantity around different two points in parameter space. In terms of the two perturbative expansions, we introduce a new type of smooth interpolating function consistent with the both expansions, which includes the standard Padé approximant and fractional power of polynomial method constructed by Sen as special cases. We point out that we can construct enormous number of such interpolating functions in principle while the "best" approximation for the exact answer of the physical quantity should be unique among th…
We show that the one-loop quantum deformation of the universal hypermultiplet provides a family of complete $1/4$-pinched negatively curved quaternionic Kähler (i.e. half conformally flat Einstein) metrics $g^c$, $c\ge 0$, on $\mathbb R^4$. The metric $g^0$ is the complex hyperbolic metric whereas the family $(g^c)_{c>0}$ is equivalent to a family of metrics $(h^b)_{b>0}$ depending on $b=1/c$ and smoothly extending to $b=0$ for which $h^0$ is the real hyperbolic metric. In this sense the one-loop deformation interpolates between the real and the complex hyperbolic metrics. We also determine th…
We introduce a more general set of kinematic renormalization schemes than the original momentum (MOM) subtraction schemes of Celmaster and Gonsalves. These new schemes will depend on a parameter $ω$ which tags the external momentum of one of the legs of the $3$-point vertex functions in Quantum Chromodynamics (QCD). In each of the three new schemes we renormalize QCD in the Landau and maximal abelian gauges and establish the three loop renormalization group functions in each gauge. As an application we evaluate two critical exponents at the Banks-Zaks fixed point and demonstrate that their val…
The 't Hooft model, i.e. the two-dimensional quantum chromodynamics in the limit of infinite number of colors, is interpolated by an angle parameter $δ$ between $δ=0$ for the instant form dynamics (IFD) and $δ=π/4$ for the light-front dynamics (LFD). With this parameter $δ$, we formulate the interpolating mass gap equation which takes into account the non-trivial vacuum effect on the bare fermion mass to find the dressed fermion mass. Our interpolating mass gap solutions link the IFD and LFD results with the $δ$ parameter. We find the interpolation angle independent characteristic energy funct…
We study the behavior of the effective potential between revolving D$p$-branes at all ranges of the distance $r$, interpolating $r \gg l_s$ and $r \ll l_s$ ($l_s$ is the string length). Since the one-loop open string amplitude cannot be calculated exactly, we instead employ an efficient method of $\it{ partial\ modular\ transformation}$. The method is to perform the modular transformation partially in the moduli parameter and rewrite the amplitude into a sum of contributions from both of the open and closed string massless modes. It is nevertheless free from the double counting and can approxi…
We take into account higher derivative R4 corrections in M-theory and construct quantum black hole and black string solutions in 11 dimensions up to the next leading order. The quantum black string is stretching along the 11th direction and the Gregory-Laflamme instability is examined at the quantum level. Thermodynamics of the boosted quantum black hole and black string are also discussed. Especially we take the near horizon limit of the quantum black string and investigate its instability quantitatively.
