arXiv subjects

K. S. Narain

Publications and source records attributed to K. S. Narain.

At least 37 records · Page 2Linked to original sources

arXiv2007

Harmonicity in N=4 supersymmetry and its quantum anomaly

The holomorphicity property of N=1 superpotentials or of N=2 F-terms involving vector multiplets is generalized to the case of N=4 1/2-BPS effective operators defined in harmonic superspace. The resulting harmonicity equations are shown to control the moduli dependence of the couplings of higher dimensional operators involving powers of the N=4 Weyl superfield, computed by N=4 topological amplitudes. These equations can also be derived on the string side, exhibiting an anomaly from world-sheet boundary contributions that leads to recursion relations for the non-analytic part of the couplings.

hep-th↗

arXiv2007

1/8 BPS States in Ads/CFT

We study a class of exact supersymmetric solutions of type IIB Supergravity. They have an SO(4) x SU(2) x U(1) isometry and preserve generically 4 of the 32 supersymmetries of the theory. Asymptotically AdS_5 x S^5 solutions in this class are dual to 1/8 BPS chiral operators which preserve the same symmetries in the N=4 SYM theory. They are parametrized by a set of four functions that satisfy certain differential equations. We analyze the solutions to these equations in a large radius asymptotic expansion: they carry charges with respect to two U(1) KK gauge fields and their mass saturates the expected BPS bound.

hep-th↗

arXiv2007

BPS Solutions in AdS/CFT

We study a class of exact supersymmetric solutions of type IIB Supergravity. They have an SO(4) x SU(2) x U(1) isometry and preserve generically 4 of the 32 supersymmetries of the theory. Asymptotically AdS_5 x S^5 solutions in this class are dual to 1/8 BPS chiral operators which preserve the same symmetries in the N=4 SYM theory. We analyse the solutions to these equations in a large radius asymptotic expansion: they carry charges with respect to two U(1) KK gauge fields and their mass saturates the expected BPS bound. We also show how the same formalism is suitable for the description of the AdS_5 x Y^{p,q} geometries and a class of their excitations.

hep-th↗

arXiv2006

N=4 Topological Amplitudes and String Effective Action

Certain scattering amplitudes in the gravitational sector of type II string theory on K3 x T^2 are found to be computed by correlation functions of the N=4 topological string. This analysis extends the already known results for K3 by Berkovits and Vafa, which correspond to six-dimensional terms in the effective action, involving four Riemann tensors and 4g-4 graviphotons, R^4T^{4g-4}, at genus g. We find two additional classes of topological amplitudes that use the full internal SCFT of K3 x T^2. One of these string amplitudes is mapped to a 1-loop contribution in the heterotic theory, and is studied explicitly. It corresponds to the four-dimensional term R^2(ddΦ)^2T^{2g-4}, with Φa Kaluza-Klein graviscalar from T^2. Finally, the generalization of the harmonicity relation for its moduli dependent coupling coefficient is obtained and shown to contain an anomaly, generalizing the holomorphic anomaly of the N=2 topological partition function F_g.

hep-th↗

arXiv2006

Towards a string bit formulation of N=4 super Yang-Mills

We show that planar cal N=4 Yang-Mills theory at zero 't Hooft coupling can be efficiently described in terms of 8 bosonic and 8 fermionic oscillators. We show that these oscillators can serve as world-sheet variables, the string bits, of a discretized string. There is a one to one correspondence between the on shell gauge invariant words of the free Y-M theory and the states in the oscillators' Hilbert space, obeying a local gauge and cyclicity constraints. The planar two-point functions and the three-point functions of all gauge invariant words are obtained by the simple delta-function overlap of the corresponding discrete string world sheet. At first order in the 't Hooft coupling, i.e. at one-loop in the Y-M theory, the logarithmic corrections of the planar two-point and the three-point functions can be incorporated by nearest neighbour interactions among the discretized string bits. In the SU(2) sub-sector we show that the one-loop corrections to the structure constants can be uniquely determined by the symmetries of the bit picture. For the SU(2) sub-sector we construct a gauged, linear, discrete world-sheet model for the oscillators, with only nearest neighbour couplings, which reproduces the anomalous dimension Hamiltonian up to two loops. This model also obeys BMN scaling to all loops.

hep-th↗

arXiv2005

Open string topological amplitudes and gaugino masses

We discuss the moduli-dependent couplings of the higher derivative F-terms $(\Tr W^2)^{h-1}$, where $W$ is the gauge N=1 chiral superfield. They are determined by the genus zero topological partition function $F^{(0,h)}$, on a world-sheet with $h$ boundaries. By string duality, these terms are also related to heterotic topological amplitudes studied in the past, with the topological twist applied only in the left-moving supersymmetric sector of the internal $N=(2,0)$ superconformal field theory. The holomorphic anomaly of these couplings relates them to terms of the form $Π^n({\rm Tr}W^2)^{h-2}$, where $Π$'s represent chiral projections of non-holomorphic functions of chiral superfields. An important property of these couplings is that they violate R-symmetry for $h\ge 3$. As a result, once supersymmetry is broken by D-term expectation values, $(\Tr W^2)^2$ generates gaugino masses that can be hierarchically smaller than the scalar masses, behaving as $m_{1/2}\sim m_0^4$ in string units. Similarly, $Π{\rm Tr}W^2$ generates Dirac masses for non-chiral brane fermions, of the same order of magnitude. This mechanism can be used for instance to obtain fermion masses at the TeV scale for scalar masses as high as $m_0\sim{\cal O}(10^{13})$ GeV. We present explicit examples in toroidal string compactifications with intersecting D-branes.

hep-th↗

arXiv2005

Structure constants of planar N =4 Yang Mills at one loop

We study structure constants of gauge invariant operators in planar N=4 Yang-Mills at one loop with the motivation of determining features of the string dual of weak coupling Yang-Mills. We derive a simple renormalization group invariant formula characterizing the corrections to structure constants of any primary operator in the planar limit. Applying this to the scalar SO(6) sector we find that the one loop corrections to structure constants of gauge invariant operators is determined by the one loop anomalous dimension Hamiltonian in this sector. We then evaluate the one loop corrections to structure constants for scalars with arbitrary number of derivatives in a given holomorphic direction. We find that the corrections can be characterized by suitable derivatives on the four point tree function of a massless scalar with quartic coupling. We show that individual diagrams violating conformal invariance can be combined together to restore it using a linear inhomogeneous partial differential equation satisfied by this function.

hep-th↗

arXiv2005

Spacetime Properties of ZZ D-Branes

We study the tachyon and the RR field sourced by the $(m,n)$ ZZ D-branes in type 0 theories using three methods. We first use the mini-superspace approximation of the closed string wave functions of the tachyon and the RR scalar to probe these fields. These wave functions are then extended beyond the mini-superspace approximation using mild assumptions which are motivated by the properties of the corresponding wave functions in the mini-superspace limit. These are then used to probe the tachyon and the RR field sourced. Finally we study the space time fields sourced by the $(m,n)$ ZZ D-branes using the FZZT brane as a probe. In all the three methods we find that the tension of the $(m,n)$ ZZ brane is $mn$ times the tension of the $(1,1)$ ZZ brane. The RR charge of these branes is non-zero only for the case of both $m$ and $n$ odd, in which case it is identical to the charge of the $(1,1)$ brane. As a consistency check we also verify that the space time fields sourced by the branes satisfy the corresponding equations of motion.

hep-th↗

arXiv2003

Partial ${\cal N}=2 \to {\cal N}=1$ supersymmetry breaking and gravity deformed chiral rings

We present a derivation of the chiral ring relations, arising in ${\cal N}=1$ gauge theories in the presence of (anti-)self-dual background gravitational field $G_{αβγ}$ and graviphoton field strength $F_{αβ}$. These were previously considered in the literature in order to prove the relation between gravitational F-terms in the gauge theory and coefficients of the topological expansion of the related matrix integral. We consider the spontaneous breaking of ${\cal N} =2$ to ${\cal N} =1$ supergravity coupled to vector- and hyper-multiplets, and take a rigid limit which keeps a non-trivial $G_{αβγ}$ and $F_{αβ}$ with a finite supersymmetry breaking scale. We derive the resulting effective, global, ${\cal N}=1$ theory and show that the chiral ring relations are just a consequence of the standard ${\cal N}=2$ supergravity Bianchi identities . We can also obtain models with matter in different representations and in particular quiver theories. We also show that, in the presence of non-trivial $F_{αβ}$, consistency of the Konishi-anomaly loop equations with the chiral ring relations, demands that the gauge kinetic function and the superpotential, a priori unrelated for an ${\cal N}=1$ theory, should be derived from a prepotential, indicating an underlying ${\cal N}=2$ structure.

hep-th↗

arXiv2003

Gravitational F-terms through anomaly equations and deformed chiral rings

We study effective gravitational F-terms, obtained by integrating an $U(N)$ adjoint chiral superfield $Φ$ coupled to the ${\cal N}=1$ gauge chiral superfield $W_α$ and supergravity, to arbitrary orders in the gravitational background. The latter includes in addition to the ${\cal N}=1$ Weyl superfield $G_{αβγ}$, the self-dual graviphoton field strength $F_{αβ}$ of the parent, broken ${\cal N}=2$ theory. We first study the chiral ring relations resulting from the above non-standard gravitational background and find agreement, for gauge invariant operators, with those obtained from the dual closed string side via Bianchi identities for ${\cal N}=2$ supergravity coupled to vector multiplets. We then derive generalized anomaly equations for connected correlators on the gauge theory side, which allow us to solve for the basic one-point function $\langle {\rm Tr} W^2/(z-Φ)\rangle$ to all orders in $F^2$. By generalizing the matrix model loop equation to the generating functional of connected correlators of resolvents, we prove that the gauge theory result coincides with the genus expansion of the associated matrix model, after identifying the expansion parameters on the two sides.

hep-th↗

arXiv2003

Konishi anomaly approach to gravitational F-terms

We study gravitational corrections to the effective superpotential in theories with a single adjoint chiral multiplet, using the generalized Konishi anomaly and the gravitationally deformed chiral ring. We show that the genus one correction to the loop equation in the corresponding matrix model agrees with the gravitational corrected anomaly equations in the gauge theory. An important ingrediant in the proof is the lack of factorization of chiral gauge invariant operators in presence of a supergravity background. We also find a genus zero gravitational correction to the superpotential, which can be removed by a field redefinition.

hep-th↗

arXiv2002

Proving the PP-Wave/CFT_2 Duality

We study the duality between IIB string theory on a pp-wave background, arising as a Penrose limit of the AdS_3 times S^3 times M, where M is T^4 (or K3), and the 2D CFT which is given by the N=(4,4) orbifold (M)^N/S_N, resolved by a blowing-up mode. After analizying the action of the supercharges on both sides, we establish a correspondence between the states of the two theories. In particular and for the T^4 case, we identify both massive and massless oscillators on the pp-wave, with certain classes of excited states in the resolved CFT carrying large R-charge n. For the former, the excited states involve fractional modes of the generators of the N=4 chiral algebra acting on the Z_n ground states. For the latter, they involve, fractional modes of the U(1)^4_L times U(1)^4_R super-current algebra acting on the Z_n ground states. By using conformal perturbation theory we compute the leading order correction to the conformal dimensions of the first class of states, due to the presence of the blowing up mode. We find agreement, to this order, with the corresponding spectrum of massive oscillators on the pp-wave. We also discuss the issue of higher order corrections.

hep-th↗

arXiv2002

Open Strings on Plane waves and their Yang-Mills duals

We study the plane wave limit of $AdS_5\times S^5/Z_2$ which arises as the near horizon geometry of D3-branes at an orientifold 7-plane in type I' theory. We analyze string theory in the resulting plane wave background which contains open strings. We identify gauge invariant operators in the dual $Sp(N)$ gauge theory with unoriented closed and open string states.

hep-th↗

arXiv2002

Little String Theories in Heterotic Backgrounds

We study Little String Theories (LST) with ${\cal N}=(1,0)$ supersymmetry arising, in a suitable double scaling limit, from 5-branes in heterotic string theory or in the heterotic-like type II/$(-)^{F_L}\times {\rm shift}$. The limit in question, previously studied in the type II case, is such that the resulting holographically dual pairs, i.e. bulk string theory and LST are at a finite effective coupling. In particular, the internal $(2,2)$ SCFT on the string theory side is non-singular and given by $SL(2)/U(1)\times SU(2)/U(1)$ coset. In the type II orbifold case, we determine the orbifold action on the internal SCFT and construct the boundary states describing the non-BPS massive states of a completely broken $SO$ gauge theory, in agreement with the dual picture of D5-branes in type II/$Ω\times {\rm shift}$. We also describe a different orbifold action which gives rise to a $Sp$ gauge theory with $(1,1)$ supersymmetry. In both the heterotic SO(32) and $E_8\times E_8$ cases, we determine the gauge bundles which correspond to the above SCFT and break down the gauge groups to $SU(2)\times SO(28)$ and $E_7\times E_8$ respectively. The double scaling limit in this case involves taking small instanton together with small string coupling constant limit. We determine the spectrum of chiral gauge invariant operators with the corresponding global symmetry charges on the LST side and compare with the massless excitations on the string theory side, finding agreement for multiplicities and global charges.

hep-th↗

arXiv2001

Instantons, the Information Metric, and the AdS/CFT Correspondence

We describe some remarkable properties of the so-called Information Metric on instanton moduli space. This Metric is manifestly gauge and conformally invariant and coincides with the Euclidean AdS_5 metric on the one-instanton SU(2) moduli space for the standard metric on R^4. We propose that for an arbitrary boundary metric the AdS/CFT bulk space-time is the instanton moduli space equipped with the Information Metric. To test this proposal, we examine the variation of the instanton moduli and the Information Metric for first-order perturbations of the boundary metric and obtain three non-trivial and somewhat surprising results: (1) The perturbed Information Metric is Einstein. (2) The perturbed instanton density is the corresponding massless boundary-to-bulk scalar propagator. (3) The regularized boundary-to-bulk geodesic distance is proportional to the logarithm of the perturbed instanton density. The Hamilton-Jacobi equation implied by (3) equips the moduli space with a rich geometrical structure which we explore. These results tentatively suggest a picture in which the one-instanton sector of SU(2) Yang-Mills theory (rather than some large-N limit) is in some sense holographically dual to bulk gravity.

hep-th↗

arXiv2001

AdS/CFT correspondence and D1/D5 systems in theories with 16 supercharges

We discuss spectra of $AdS_3$ supergravities, arising in the near horizon geometry of D1/D5 systems in orbifolds/orientifolds of type IIB theory with 16 supercharges. These include models studied in a recent paper (hep-th/0012118), where the group action involves also a shift along a transversal circle, as well as IIB/$ΩI_4$, which is dual to IIB on $K3$. After appropriate assignements of the orbifold group eigenvalues and degrees to the supergravity single particle spectrum, we compute the supergravity elliptic genus and find agreement, in the expected regime of validity, with the elliptic genus obtained using U-duality map from (4,4) CFTs of U-dual backgrounds. Since this U-duality involves the exchange of KK momentum $P$ and D1 charge $N$, it allows us to test the (4,4) CFTs in the $P < N/4$ and $N < P/4$ regimes by two different supergravity duals.

hep-th↗

arXiv2000

D1/D5 systems in ${\cal N}=4$ string theories

We propose CFT descriptions of the D1/D5 system in a class of freely acting Z_2 orbifolds/orientifolds of type IIB theory, with sixteen unbroken supercharges. The CFTs describing D1/D5 systems involve N=(4,4) or N=(4,0) sigma models on $(R^3\times S^1\times T^4\times (T^4)^N/S_N)/Z_2$, where the action of Z_2 is diagonal and its precise nature depends on the model. We also discuss D1(D5)-brane states carrying non-trivial Kaluza-Klein charges. The resulting multiplicities for two-charge bound states are shown to agree with the predictions of U-duality. We raise a puzzle concerning the multiplicities of three-charge systems, which is generically present in all vacuum configurations with sixteen unbroken supercharges studied so far, including the more familiar type IIB on K3 case: the constraints put on BPS counting formulae by U-duality are apparently in contradiction with any CFT interpretation. We argue that the presence of RR backgrounds appearing in the symmetric product CFT may provide a resolution of this puzzle.

hep-th↗

arXiv1999

Instantons in ${\cal N}=2$ $Sp(N)$ Superconformal Gauge Theories and the AdS/CFT Correspondence

We study, using ADHM construction, instanton effects in an ${\CN}=2$ superconformal $Sp(N)$ gauge theory, arising as effective field theory on a system of $N$ D-3-branes near an orientifold 7-plane and 8 D-7-branes in type I' string theory. We work out the measure for the collective coordinates of multi-instantons in the gauge theory and compare with the measure for the collective coordinates of $(-1)$-branes in the presence of 3- and 7-branes in type I' theory. We analyse the large-N limit of the measure and find that it admits two classes of saddle points: In the first class the space of collective coordinates has the geometry of $AdS_5\times S^3$ which on the string theory side has the interpretation of the D-instantons being stuck on the 7-branes and therefore the resulting moduli space being $AdS_5\times S^3$, In the second class the geometry is $AdS_5\times S^5/Z_2$ and on the string theory side it means that the D-instantons are free to move in the 10-dimensional bulk. We discuss in detail a correlator of four O(8) flavour currents on the Yang-Mills side, which receives contributions from the first type of saddle points only, and show that it matches with the correlator obtained from $F^4$ coupling on the string theory side, which receives contribution from D-instantons, in perfect accord with the AdS/CFT correspondence. In particular we observe that the sectors with odd number of instantons give contribution to an O(8)-odd invariant coupling, thereby breaking O(8) down to SO(8) in type I' string theory. We finally discuss correlators related to $R^4$, which receive contributions from both saddle points.

hep-th↗